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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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