Question 13

The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares?

Solution

$$x+y=14\ and\ x^2-y^2=56\ .$$

So, $$x-y=4\ .$$

So, $$x-y+x+y=4+14\ .$$

or, $$x=\frac{18}{2}=9\ .$$

So, $$y=5\ .$$

So, $$x^2+y^2=9^2+5^2=81+25=106\ .$$

A is correct choice.

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