The difference of two positive numbers is 4 and the difference of their squares is 64.
Form equations and find the larger number using factorisation.

Question

The difference of two positive numbers is 4 and the difference of their squares is 64. Form equations and find the larger number using factorisation.

Accepted Answer

10. a - b = 4 and a^2 - b^2 = 64. Since a^2 - b^2 = (a-b)(a+b) = 4(a+b) = 64, a + b = 16. With a - b = 4, a = 10, b = 6. Larger number is 10.

Step-by-Step Solution