Question

The sum of squares of three consecutive numbers is 50. Find these numbers.

Answer 1

let the numbers be x , (x+1) , (x+2)

=> according to question ,

x²+(x+1)²+(x+2)² = 50

=> x²+x²+1+2x+x²+4x+4 = 50

=> 3x²+6x+5 = 50

=> 3x²+6x = 45

=> 3(x²+2x) = 45

=> x²+2x = 45/3 => 15

=> x²+2x-15 = 0

=> x²+5x-3x-15 = 0. (splitting the middle term)

=> x(x+5)-3(x+5) = 0

=> (x+5)(x-3) = 0


=> x+5 = 0 => x= -5
if x = -5

then , 2 nos will be => x+1 => -5+1 => -4
x+2 => -5+2 => -3


x-3 = 0 => x=3

if x = 3 , then , 2 nos will be => x+1 => 3+1 => 4

and x+2 => 3+2 => 5




hope this helps

Answer 2

Hi ,

Let ( a - 1 ) , a , ( a + 1 ) are three

consecutive numbers ,

According to the problem given ,

( a - 1 )² + a² + ( a + 1 )² = 50

2(a² + 1 ) + a² = 50

2a²+ 2 + a² = 50

3a² = 48

a² = 48/3

a² = 16

a = √16

a = 4

Therefore ,

Required numbers are ,

a - 1 = 4 - 1 = 3

a = 4

a + 1 = 4 + 1 = 5

I hope this helps you.

:)