Question

the sum of squares of two consecutive natural numbers is 685. Find the numbers

Answer 1

Let the first no. be x and second no. be x+1
A/Q x²+(x+1)² = 685
x²+x²+2x+1 = 685
2x²+2x+1 = 685
2x²+2x-684 = 0
2x²+38x-36x-684 = 0
2x(x+19)-36(x+19) = 0
(2x-36)(x+19) = 0
If 2x-36 = 0  or  x+19 = 0
2x = 36  or  x = -19
x = $\frac{36}{2} = 18$
But x∈N and -19∉N
∴ x=18

Answer 2

Let the two consecutive nos. be x and x+1

a/q

X^2 + (X+1)^2 =685

gives 18 and 19.