Question

If X= 1/x-5, find x2+1/x2

Answer 1

Answer:

( x + 1 /x ) = 5

We need to find x2 + 1 / x2

( x + 1 / x )2 = 25

= x2 + 1 / x2 + 2 (x)(1/x) = 25

= x2 + 1/x2 + 2 = 25

= x2 + 1 / x2 = 25 – 2

= x2 + 1 / x2=23

Hence x2 + 1 / x2 = 23

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Answer 2

Answer :

value of x²-1/x² is -5√29

Step - by - step Explanation :

Given : x = 1/5-5

=> x -1/x = -5

To find : x²-1/x²

We know that ( a+b )² = (a-b)²+4ab

put a=x and b=1/x

(x+1/x)² = (x-1/x)² + 4 • x • 1/x

=> (x+1/x)² = (-5)²+4

=> (x+1/x)² =25+4

=> x+1/x = √29

Now , we know that a²-b² = (a+b) (a-b)

put a=x and y = 1/x

we get ,

x²-(1/x)² = (x +1/x ) (x-1/x)

=> x² - 1/x ² = (√29) (-5)

=> x² -1/x ² = -5√29

Therefore the value of x² - 1/x² is -5√29

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