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the sum of three numbers is 14 and the sum of their squares is 100

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Mohammed

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Find three numbers in GP such that their sum is 14 and the sum of their square is 84

Click here👆to get an answer to your question ✍️ Find three numbers in GP such that their sum is 14 and the sum of their square is 84 -

Question

A

B

C

D

2,4,8

Easy Open in App Solution Verified by Toppr

Correct option is D)

Let three numbers in G.P=a,ar,ar

2

Sum of three number=14

a+ar+ar 2 =14 ……..(1)

Sum of squares of number=84

a 2 +a 2 r 2 +a 2 r 4 =84

Squaring equation (1) both sides

a 2 +a 2 r 2 +a 2 r 4 +2a 2 r+2a 2 r 3 +2a 2 r 2 =196 84+2a 2 r(1+r 2 +r)=196 2a 2 r a 14 ​ =196−84 2ar14=112 a= 14×2r 112 ​ = r 4 ​ r 4 ​ +4+4r=14 4+4r+4r 2 =14r 4r 2 −10r+4=0 2r 2 −5r+2=0 r= 4 5± 25−16 ​ ​ r= 4 5±3 ​ =2, 2 1 ​ r=2,a=2; r= 2 1 ​ ,a=8 Three terms: 2,4,8 Three terms: 8,4,2

∴ Three terms are: 2,4,8.

25 -2

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Sum of two numbers is 14 and sum of their squares is 100,what are the numbers?

Answer: Let the two numbers be x and y Sum of two numbers is 14 Therefore, x + y = 14 …(1) Sum of the squares of these two numbers is 100 Therefore, x² + y² = 100 ….(2) From the equation (2), we get x² + y² = 100 or, 2(x² + y²) = 100×2 or, (x+y)² + (x-y)² = 200 or, 14² + (x-y)² = 200 or,...

Sum of two numbers is 14 and sum of their squares is 100,what are the numbers?

Teacher at The High School Experience (2011–present)1y

Let the two numbers be x and y

Sum of two numbers is 14

Therefore, x + y = 14 …(1)

Sum of the squares of these two numbers is 100

Therefore, x² + y² = 100 ….(2)

From the equation (2), we get x² + y² = 100

or, 2(x² + y²) = 100×2

or, (x+y)² + (x-y)² = 200

or, 14² + (x-y)² = 200

or, 196 + (x-y)² = 200

or, (x-y)² = 200 — 196

or, (x-y)² = 4 or, (x-y) = 2, —2

If x-y =2, then we get x+y+x-y = 14+2

or, 2x = 16 or, x = 16/2 or, x= 8 So, y= 14–8 = 6

If x-y = —2, then we get x+y+x-y = 14–2

or, 2x = 12 or, x= 12/2 or, x = 6 So, y = 14–6 = 8

Hence, the required two numbers are 8,6 or 6,8 respectively.

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the sum of three numbers is 14 and sum of their square is 100 find the sum of cubes of their numbers

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