1.

IF X∧2+1/X∧2=7 , FIND THE VALUE OF X∧3+1/X∧3PLS ANSWER ITS AN EMERGENCY

Answer» HI !

So,

{x}^{2} + \frac{1}{ {x}^{2} } = 7 \\

We can WRITE it as,

{x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\

We know that,

{a}^{2} + {<klux>B</klux>}^{2} + 2ab = {(a + b)}^{2} \\

Assuming a = x
and b = 1/x

We can write,

{(x + \frac{1}{x} )}^{2} = {(3)}^{2} \\ \\ x + \frac{1}{x} = 3

CUBING both the SIDES we get,

{(x + \frac{1}{x}) }^{3} = {(3)}^{3} \\

Using the identity :

{(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\

{(x)}^{3} + {( \frac{1}{x} )}^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 27\\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(3) = 27 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 9 = 27 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 27 - 9 \\ \\ {x}^{3} + \frac{1}{{x}^{3} } = 18

Any doubt arises, please ask ^-^


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