Question

The arithmetic mean (average) of the numbers a and 6 is 5, and the geometric mean of the numbers a and b is 8. Then a2 − 10a =
(A) −64
(B) 76
(C) 82
(D) 96
(E) 102

Answer 1

Recall the arithmetic mean of two numbers \(x_1,x_2\) is given by \(\frac{x_1+x_2}2\). Similarly, the geometric mean is \(\sqrt{x_1x_2}\).