Question

If x square+1/x=4 find the value of 2x cube +2/x cube​

Answer 1

Given :  a² + 1/a²  = 4

To Find :   (2a)³  + (2/a)³

Solution:

a has been taken instead of x  

a² + 1/a²  = 4

=> a² + 1/a²  + 2a(1/a) = 4 + 2a(1/a)

=> (a + 1/a)² = 4 + 2

=> a + 1/a  = √6

=> a² + 1/a²  - 2a(1/a) = 4 - 2a(1/a)

=> (a - 1/a)² = 4 - 2

=> a - 1/a  = √2

a + 1/a  = √6

a - 1/a  = √2

=> 2a = √6 + √2

=> 2/a =  √6 - √2

(2a)³  + (2/a)³  = (√6 + √2)³  + (√6 - √2)³

x³ + y³ = (x + y)(x²  + y²  - xy)

x= √6 + √2  , y = √6  - √2

=  (√6 + √2 + √6  - √2) (  (√6 + √2)² + (√6 - √2)²  -  (√6 + √2) (√6 - √2))

=  2√6(6 + 2 + 2√12 + 6 + 2 - 2√12  - (6 - 2))

=   2√6(16  - 4)

= 2√6(12)

= 24√6

Learn More:

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