Question

if the expression 16x^4 - 24x^3 +41x^2 – nx +16 is a perfect square then the value of ‘n’ is

Answer 1

The equation is 

 16x^4 - 24x^3 + 41x^2 -nx +16

 (4x^2)^2 - 2 * 4x^2 * 3x + 9x^2 + 32x^2 -nx + 4^2

 Now, on comparing with the general formula of (a + b + c)^2
 We find a = 4x^2
             b = -3x
             c = 4
 So, 
 it has to be
 (4x^2)^2 - 2 * 4x^2 * 3x + 9x^2 + 32x^2 -2 * 3x * 4 + 4^2

 or n = 2*3*4
        = 24