Question

please solve this urgently​

Answer 1

Answer:

x = 3 or 1/3 or ( 7 + √13 ) / 6 or ( 7 - √13 ) / 6

Step-by-step explanation:

Given----->

9 ( x² + 1 / x² ) - 9 ( x + 1 / x ) - 52

To find------> Value of x

Solution-----> 1) Plzzz see the attachment

2) First we suppose

x + 1/x = y

Squaring both sides , we get,

=> ( x + 1 / x )² = y²

=> x² + 1 / x² + 2 x ( 1 / x ) = y²

=> x² + 1 / x² + 2 = y²

=> x² + 1 / x² = y² - 2

putting these values in original equation , we get

9 y² - 9 y - 70 = 0

3) Now we factorise it by splitting the middle term , we get ,

( 3y - 10 ) ( 3y + 7 ) = 0

Now , if ,

3 y - 10 = 0

Now putting y = x + 1 / x , we get,

3 x² -10x + 3 = 0

Solving it we get ,

x = 3 or 1/3

4) Now if , 3y + 7 = 0

Putting y = x + 1 / x , we get ,

3x² - 7x + 3 = 0

By solving it we get ,

x = ( 7 + √13 ) / 6 or ( 7 - √13 ) / 6