Value of n is 6
4. 6 x4 + 4x3 + nx2 + 4x + 1= (ax2 + bx + c)2 x4 + 4x3 + nx2 + 4x + 1 = a2 x4 + b2 x2 + c2 +2abx3 + 2bcx + 2acx2 = a2 x4 + 2abx3 + (b2 + 2ac ) x2 + 2bcx + c2 Comparing coefficients, a2 = 1 c2 = 1 2ab = 4 b2 + 2 ac = n 2bc = 4 Solving, we get a/c = 1 ⇒ a = c b = \(\pm\)2 , a = \(\pm\)1 , c = \(\pm\)1 ∴ b2 + 2ac = 4 + 2 = 6
The-value-of-n-for-which-the-expression-x-4-4x-3-nx-2-4x-1becomes-a-perfect-square-is 6
