If the sum of the squares of two positive numbers is 170 and their product is 77, what is the difference of their squares?

Correct answer: c 72

(x² − y²)² = 170² − 4·77² = 28900 − 23716 = 5184; the difference of squares is 72 (the numbers are 11 and 7).

Why the other options are wrong

• a 18: 18 = x + y (11 + 7); the difference of squares is 121 − 49 = 72.
• b 51: 51 does not come from any step; (x² − y²)² = 28900 − 23716 = 5184 and the difference of squares is 72.
• d 85: 85 is 170/2; the difference of squares is 72.