Question

if 2x-1/2 x=2 then the value of 16x^4+1/16^4 is

Answer 1

2x-1/x=6

on squaring

(2x-1/x)²=6²

4x²-2*2x*1/x+1/x²=36

4x²-4+1/x²=36

4x²+1/x²=36+4=40

on squaring

(4x²+1/x²)²=40²

16x^4+4x²*2*1/x²+1/x^4=1600

16x^4+1/x^4=1600 - 8=1592

and the answer is 1592

Answer 2

2x-1 / 2x = 2

2x-1 = (2)(2x)

2x-1 = 4x

2x = -1

x = -1/2

Now , it is given that,

16x⁴ + 1/16⁴

Putting value of x

16(-1/2)⁴ + 1/16

= 16(1/16) + 1/16

= 1 + 1/16

Taking LCM,

= 16 + 1 / 16

= 17/16

Therefore 17/16 is your answer

HOPE IT HELPS YOU!!