Question

solve x/x-1 + x-1 by x = 17/4​

Answer 1

Answer:

+4/3

-1/3

Step-by-step explanation:

Given an equation such that,

x/(x-1) + (x-1)/x = 17/4

To solve it.

Let's assume that,

x/(x-1) = u

Therefore, we have,

=> u+ 1/u = 17/4

=> (u^2+1)/u = 17/4

=> 4(u^2+1) = 17u

=> 4u^2 + 4 = 17u

=> 4u^2 - 17u + 4 = 0

=> 4u^2 - 16u - u + 4 = 0

=> 4u(u-4)-1(u-4) = 0

=> (u-4)(4u-1) = 0

Therefore, we have,

=> u - 4 = 0

=> u = 4

And

=> 4u -1 = 0

=> u = ¼

Thus, we have,

=> x/(x-1) = 4

=> x = 4(x-1)

=> x = 4x-4

=> 3x = 4

=> x = 4/3

And

=> x/(x-1) = ¼

=> 4x = x - 1

=> 3x = -1

=> x = -⅓

Hence, the values of x are 4/3 and -1/3.

Answer 2

Answer:

x+1/x =17/4

Square on both sides,

(x+1/x)²=(17/4)²

x²+1/x² +2= (289/16)

x²+1/x² =289/16 -2

x² +1/x² = (289-32)/16

x² +1/x² =257/16

Now,

Subtract 2(x*1/x) from both sides,

x²+1/x² -2 =(257/16) -2

______________________

By formula (a-b)²=a²+b² -2ab

______________________

(x-1/x)² =(257-32)/16

(x-1/x)² = 225/16

(x-1/x)² =(15/4)²

x-1/x =15/4

I hope this will help you .......

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