if x-1/x = 1/2, then write the value of 4x^2 + 4/x^2 - Maths - Number Systems

Question

if x-1/x = 1/2, then write the value of 4x^2 +
4/x^2

Swagat Swargari · Accepted Answer

x-1/x=1/2
(x-1/x)2 =(1/2)2 (Squaring both sides)
x2 + 1/x2 -2 x 1/x = 1/4
x2 + 1/x2 -2 =1/4
x2+ 1/x2= 1/4 + 2
x2+1/x2= 9/4 ------equation (1)

Now, 4x^2 + 4/x^2
= 4(x^2 + 1/x^2)
=4 * 9/4 (from equation (1))
=9