The harmonic mean of two numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A +G2 = 27. Find the numbers.
Determine the sum of imaginary roots of the equation (2x + x - 1) ( 4x2 + 2x - 3) = 6
Given, (2x + x - 1) ( 4x2 + 2x - 3) = 6
Put 2x2 + x = y
Discriminants,
D1 = 1 + 4 x 3 = 13 > 0, real roots
D2 = 4 - 16 = - 12 < 0, imaginary roots
Sum of roots of 4x + 2x + 1 = 0 is
If cos(A) + cos(B) + cos(C) = 0, prove that
cos(3A) + cos(3B) + cos(3C) = 12 cos(A) cos(B)cos(C)
Let IR be the set of real numbers and f : IR ➔ IR be such that for all x, y ∈ IR, . Prove that f is a constant function.