Permutations and Combinations

Question

# Find four numbers in GP. whose sum is 85 and product is 4096.

Let the four numbers in G.P. be
Since their product is 4096.

∴

Since their sum is 85

∴

Put
∴        or

Putting                               2t = x, we get

By inspection x = 5 satisfies the equation. So x - 5 is a factor of . Other roots are given by

x is imaginary
∴      x = 5 is the only real value
So,                       2t = 5,

When a = 8, r = 2, numbers are
When a = 8,  numbers are   or 64, 16, 4, 1