Question

The sum of the squares of two consecutive positive even numbers is 3364. What are the two numbers?

(a) 40, 42

(b) 38, 40

(c) 42, 44

(d) 44, 46

This question was addressed to me in an internship interview.

The doubt is from Solution of Quadratic Equation by Factorisation topic in portion Quadratic Equation of Mathematics – Class 10

Answer 1

Right answer is (a) 40, 42

For explanation: Let one number be x. The other number is x+2

Sum of the squares of the numbers is 3364.

x^2+(x+2)^2=3364

x^2+x^2+4x+4=3364

2x^2+4x-3360=0

x^2+2x-1680=0

x^2+42x-40x-1680=0

x(x+42)-40(x+42)=0

(x+42)(x-40)=0

x=40, -42

Since we only need positive numbers.

Hence, x=40

The two numbers are 40, 42.