Question

The sum of three number in G.P. is 31 and the sum of their square is 651. find the numbers

Answer 1

please refer to me if any problem

Answer 2

Answer:

The Numbers are 1, 5, 25

Step-by-step explanation:

Hey Mate,

Given Data,

a + ar + ar² = 31   .................(1)

a² + a²r² + a²r⁴ = 651       ..................(2)

Square the Eq(1)

a² + a²r² + a²r⁴ + 2(a²r + a²r³ + a²r²) = 961

a² + a²r² + a²r⁴ + 2r(a² + a²r² + a²r) = 961    .........Put the value of Eq(2)

651 + 2r(a² + a²r² + a²r) = 961

2r(a² + a²r² + a²r) = 310

2ar(a + ar² + ar) = 310   ............Put the value of Eq(1)

2ar(31) = 310

ar = 5

a = 5/r

From Eq(1)

a + ar + ar² = 31

a(1 + r + r²) = 31

5/r(1 + r + r²) = 31

1/r(1 + r + r²) = 31/5

1/r + 1 + r = 31/5

1 + r + r² = 31r/5

5 + 5r + 5r² = 31r

5r² −26r + 5 = 0

Solving this Quadratic equation we get, r = 5

a = 5/r =1

So, Those three numbers are => 1,5,25