Question

If the sum of squares of two consecutive natural numbers is 61 then what are the numbers

Answer 1

let the number be x
other number would be (x+1)

according to question ,

=> x²+(x+1)² = 61

=> x²+x²+2x+1 = 61
$(x + y)^{2} = {x}^{2} + {y}^{2} + 2xy$

=> 2x²+2x = 61-1

=> 2(x²+x) = 60

=> x²+x = 60/2 => 30


=> x²+x-30 = 0

=> x²+6x-5x-30 = 0

=> x(x+6)-5(x+6) = 0

=> (x+6)(x-5) = 0

=> (x+6) = 0
=> x = -6

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


if x = -6
then , x+1 => -6+1 => -5


if x = 5
then , x+1 => 5+1 => 6



hope this helps

Answer 2

Refer the attachment.