Math, asked by prathapjollyguy650, 11 months ago

If x-1/x=4 then the value of x+1/x is

Answers

Answered by rishu6845

Answer:

x + 1 / x = 2√5

Step-by-step explanation:

Given---> x - 1 / x = 4

To find ---> Value of x + 1 /x

Solution---> ATQ,

x - 1 /x = 4

Squaring both sides we get,

=> ( x - 1 / x )² = ( 4 )²

We know that,

( a + b )² = a² + b² + 2ab , applying it here,

=> x² + ( 1 / x² ) - 2 x ( 1 / x ) = 16

=> x² + 1 / x² - 2 = 16

=> x² + 1 / x² = 16 + 2

=> x² + 1 / x² = 18

Now , we have an identity,

( a - b )² = a² + b² - 2ab , we get,

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

= x² + 1 / x² + 2

= ( x² + 1 / x² ) + 2

= ( 18 ) + 2

( x + 1 / x )² = 20

Taking square root of both sides

=> x + 1 / x = √20

=> x + 1 / x = √4 × 5

=> x + 1 / x = 2 √5

Answered by Aɾꜱɦ

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