Question

If 16x+1 =64/4x
the value of x​

Answer 1

hope this will help you ☺️

Answer 2

Given:

16x+1 =64/4x

To find:

The value of x

Solution:

The required values of x are x = -1/32 - (5 $\sqrt{41}$)/32 and x = (5 $\sqrt{41}$)/32 - 1/32.

Solving the given equation,

16x+1 =64/4x

16x+1=16/x

(16x+1)x=16

16$x^{2}$+x=16

16$x^{2}$+x-16=0

Dividing the equation by 16,

$x^{2}$+x/16-1=0

Now we will add a number on each side to complete the square.

Adding 1/$32^{2}$ on both sides,

$x^{2}$+x/16+1/1024-1=1/1024

$(x+1/32)^{2}$-1025/1024=0

We will obtain the determinant and find the values,

The values of x= (-b+D)/2a, (-b-D)/2a

D=$b^{2}$-4ac

On solving further,

x = -1/32 - (5 $\sqrt{41}$)/32

x = (5 $\sqrt{41}$)/32 - 1/32

Therefore, the required values of x are x = -1/32 - (5 $\sqrt{41}$)/32 and x = (5 $\sqrt{41}$)/32 - 1/32.