if you want to remove an article from website contact us from top.

    how many two-digit positive integers n have the property that the sum of n and the number obtained by reversing the order of the digits of n is a perfect square?

    Mohammed

    Guys, does anyone know the answer?

    get how many two-digit positive integers n have the property that the sum of n and the number obtained by reversing the order of the digits of n is a perfect square? from screen.

    How many two digit positive integers N have the property that the sum of N and number obtained by reversing the order of the digits of N is a perfect square.

    How many two digit positive integers N have the property that the sum of N and number obtained by reversing the order of the digits of N is a perfect square.

    Byju's Answer Standard XII Mathematics

    Squaring an Inequality

    How many two ... Question

    How many two digit positive integers N have the property that the sum of N and number obtained by reversing the order of the digits of N is a perfect square.

    Open in App Solution

    Let the two digits be x and y.

    N=10x+y;

    Let M be the number obtained on reversing the digits.

    M=10y+x; N+M=10x+y+10y+x= =11x+11y=11 (x+y);

    N+M is a perfect square; i.e. 11 (x+y) is a perfect square; i.e. 11 divides the perfect square

    only 121 is divisible by 11.

    Hence M+N=121 i.e. 11 (x+y)=121

    x+y=11 and x, y are singel digit integers.

    The integer solutions to the above equation are (2,9), (3,8), (4,7), (5,6), (6,5), (7,4), (8,3), (9,2).

    Hence there are eight such two digits numbers such that the sum of the number and its reverse is a perfect square. They are 29, 38, 47, 56, 65, 74, 83, 92.

    Suggest Corrections 0

    SIMILAR QUESTIONS

    Q.

    The digit of positive integers having 3-digit number are in AP and their sum is 15 . Number obtained by reversing the digit is 594 less than the original number. Find the number.

    Q. The number N = 173889 is a perfect square The sum of the digits in

    √ N is

    Q. The sum of a two digit number and the number obtained by reversing the digits is

    66

    . If the digits of the number differ by

    2

    , find the number. How many such numbers are there?

    Q. The digits of a positive integer, having three digits are in A.P. and their sum is

    15

    . The number obtained by reversing the digits is

    594

    less than the original number. Find the number.

    Q. How many

    4

    -digit numbers are there with the property that it is a square and the number obtained by increasing all its digits by

    1 is also a square? View More EXPLORE MORE

    Squaring an Inequality

    Standard XII Mathematics

    स्रोत : byjus.com

    How many two

    Click here👆to get an answer to your question ✍️ How many two - digits positive integers N have the property that the sum of N and the number obtained by reversing the order of the digits of is a perfect square

    Class 9 >>Maths

    >>Linear Equations in Two Variable

    >>Linear Equations

    >>How many two - digits positive integers

    Question

    How many two- digits positive integers N have the property that the sum of N and the number obtained by reversing the order of the digits of  is a perfect square

    Medium Open in App

    Updated on : 2022-09-05

    Let units digit x and tens digit be y

    Solution Verified by Toppr Number=10y+x

    Reverse number=10x+y

    Sum =11x+11y =11(x+y)

    For sum to be square

    x+y=11 ∴ Number of ways= 7+2−1 C 2−1 ​ = 8 C 1 ​ =8

    Was this answer helpful?

    36 0

    स्रोत : www.toppr.com

    How many 2

    Answer (1 of 4): Firstly, I'd like to clear whether I've understood the question properly. We have to find how many 2 digit numbers which on adding with their mirror images (obtained by reversing the order of the digits) give perfect squares, are there. Positive integers are just whole numbers g...

    How many 2-digit positive integers have the property that the sum of N and the number obtained reversing the order of the digits is a perfect square?

    Ad by USAFIS

    This is the best time to apply for the Green Card DV Lottery!

    Get a chance to win and apply today! America is waiting for you with many amazing opportunities.

    Sort Syed Waquar Raza IPS Officer5y

    Let the two digits be x and y.

    N=10x+y;

    Let M be the number obtained on reversing the digits.

    M=10y+x;

    N+M=10x+y+10y+x=11x+11y=11 (x+y);

    N+M is a perfect square; i.e. 11 (x+y) is a perfect square; i.e. 11 divides the perfect square

    The maximum value of N+M can be 99+99=198;

    Consider the perfect squares series 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196. The next perfect square is 225. We need not go beyond 196 as the maximum value of N+M is 198.

    In the above aeries of perfect squares, only 121 is divisible by 11.

    Hence M+N=121 i.e. 11 (x+y)=121 i.e. x+y=11 and x, y are singe digit integers

    Related questions

    How many two-digit positive integers N have the property that the sum of N and the number obtained by reversing the order of the digits of N is a perfect square?

    The sum of a two digit number is 9 and nine times this number is twice the number obtained by reversing the order of the digits. What is the number?

    The sum of two-digit numbers and the number obtained by reversing its digits is a square number. How many such numbers are there?

    If you write all the integers from 300 to 400, how many times will you write the digit 3?

    How many two digit numbers are there, when that number is reversed and added to the original number makes a perfect square?

    Palash Saha 5y

    Firstly, I'd like to clear whether I've understood the question properly.

    We have to find how many 2 digit numbers which on adding with their mirror images (obtained by reversing the order of the digits) give perfect squares, are there. Positive integers are just whole numbers greater than zero. So we are hunting for the number (quantity) of the numbers, between 9 and 100, which on adding with their mirror images give perfect squares.

    Right? Let me continue (please inform me if I'm wrong).

    We can express any double digit number by 10x+y where x and y are 1, 2,….,8, 9, 0 (x can't be 0 as the numbe

    Sponsored by Grammarly

    Working to master your English skills?

    Grammarly can help. Get rid of typos, grammatical mistakes, and misused words with a single click!

    Anmol

    BS-MS in Fundamental Physics, Indian Institute of Science Education and Research, Pune (IISER-P) (Graduated 2020)Author has 82 answers and 407.2K answer viewsUpdated 5y

    Let Sum of the number and it's reverse: (10x+y)+(10y+x) = 11(x+y)

    For positive interger z the Given Condition:

    11(x+y)= z 2 11(x+y)=z2 =1 =1 1(x+y)= 11 2 1(x+y)=112 = x+y=11

    So All solutions for (x,y) are:

    (2,9), (3,8), (4,7), (5,6)

    All such two digit numbers are:

    29 and 92 38 and 83 47 and 74 56 and 65

    Edit: To the People asking Why

    z=11 z=11 ?

    Well, The equation is:

    11(x+y)= z 2 . 11(x+y)=z2.

    Stare at the equation for a moment!

    Your aim is to make 11(x+y) 11(x+y) a full square. 11(x+y) 11(x+y)

    is a product of two numbers:

    11 11 and (x+y). (x+y).

    You see? You already have one number 11. If other unknown number (x+y) is 11 too, then the product will become full square. Simple!

    P Nikhil Kumar

    B.Tech (ECE) from National Institute of Technology, Patna (Graduated 2022)Author has 219 answers and 629.4K answer views4y

    There are 8 such numbers.

    29, 38, 47... Gowtham Naidu

    Software Engineer (2019–present)Author has 56 answers and 712.4K answer views3y

    Related

    What is the missing Fibonacci number 144 __ 377 610?

    The Fibonacci series is the type of series in which the number is addition of last two numbers.

    In Fibonacci series the first numbers can be anything random but the 3rd number will be the sum of 1st and 2nd number and 4th number will sum of 2nd and 3rd number .

    So,in this fibonacci series

    144 ,___ ,377, 610.

    The 3rd number is 377 which will be the sum of 1st number 144 and 2nd number .

    So,

    144 + 2nd number =377

    2nd number =233

    So, the sequence will become like 144,233,377,610.

    (For recheck we can add 2nd number and 3rd number to get 4th number ie. 233+377 which gives 610 as the answer so the missing nu

    Sponsored by Forge of Empires

    Can you solve this equation in under 20 seconds?

    If so, you are likely to be in the top 5% of players in this award-winning strategic city building game.

    Bernard Montaron

    Studied Mathematics & Counting (Combinatorics) at Pierre and Marie Curie University (Graduated 1980)Author has 1.9K answers and 601.4K answer viewsUpdated 1y

    Related

    What is the sum of the digits of the positive integer n such that the number 1! · 2! · 3! · · · 2019! · 2020! /n! Is a perfect square?

    This is a great question! Thank you for asking it on Quora.

    The answer is 2, and the number is

    n=1010 n=1010

    . Here is how it goes:

    स्रोत : www.quora.com

    Do you want to see answer or more ?
    Mohammed 18 day ago
    4

    Guys, does anyone know the answer?

    Click For Answer