1.

If x+1/x = 6 ,find (I) x-1/x(ii) x²-1/x²​

Answer»

Answer :

(i) x - 1/x = 4√2

(ii) x² - 1/x² = 24√2

Solution :

GIVEN : x + 1/x = 6

To find : (i) x - 1/x , (ii) x² - 1/x²

(i) Solution :-

We know the identity -

(a - b)² = (a + b)² - 4ab

Putting a = x and b = 1/x in above identiry ,

We have ;

=> (x - 1/x)² = (x + 1/x)² - 4•x•(1/x)

=> (x - 1/x)² = 6² - 4

=> (x - 1/x)² = 36 - 4

=> (x - 1/x)² = 32

=> x - 1/x = √32

=> x - 1/x = 4√2

Hence , x - 1/x = 4√2 .

(ii) Solution :-

We know the identity -

a² - b² = (a + b)(a - b)

Putting a = x and b = 1/x in above identiry ,

We have ;

=> x² - (1/x)² = (x + 1/x)(x - 1/x)

=> x² - 1/x² = 6•4√2

=> x² - 1/x² = 24√2

Hence , x² - 1/x² = 24√2 .


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