Question

. If the average of x and 1/x be 1, then the value of 7x^10+6/x^5 will be :

Answer 1

Answer :

7x^10 + 6/x^5 = 13

Solution :

Here ,

It is given that , average of x and 1/x is 1 .

Thus ,

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

=> x + 1/x = 1•2

=> x + 1/x = 2

=> (x² + 1)/x = 2

=> x² + 1 = 2x

=> x² - 2x + 1 = 0

=> x² - 2•x•1 + 1² = 0

=> (x - 1)² = 0

=> x = 1

Now ,

=> 7x^10 + 6/x^5 = 7•1^10 + 6/1^10

=> 7x^10 + 6/x^5 = 7•1 + 6•1

=> 7x^10 + 6/x^5 = 7 + 6

=> 7x^10 + 6/x^5 = 13

Hence , 7x^10 + 6/x^5 = 13

Answer 2

Given :  average of x+1/x be 1

To Find : value of  7x^10+6/x^5

Solution:

Average of x + 1/x  = 1

=> (x  + 1/x) /2 = 1

=> (x  + 1/x)  = 2

=> x² + 1 = 2x

=> x² - 2x + 1 = 0

=> (x - 1)² = 0

=> x =  1

7x¹⁰  +   6/x⁵  =  7  +6  = 13

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