Question

Find two natural numbers which differ by 3 and the sum of whose squares is 117.​

Answer 1

Ans : 6, 9

Hint :

Let the numbers be x and x - 3. Then, x

2

+(x−3)

2

=117.

Answer 2

let the numbers are x , x+3

and

${x}^{2} + (x + 3) {}^{2} = 117 \\ {x}^{2} + {x}^{2} + 9 = 117 \\ 2 {x}^{2} = 117 - 9 \\ {2x}^{2} = 108 \\ {x}^{2} = \frac{108}{2} = 54 \\ {x}^{2} = 54$