Question

solve this dont spam
plz explain also​

Answer 1

$\underline{\boxed{\bold{Question}}}$  

$\mathtt {\rightarrow If \;( x - \dfrac{1}{x}) = 3, then \; find\;the\;value\;of ( x^3 - \dfrac{1}{x^3})}$

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$\underline{\boxed{\bold{Important\;Information}}}$  

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❏ Algebraic identities are simple formulas that leads to easy calculation for problems related to algebraic operations.

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$\underline{\boxed{\bold{Important\;Formulas}}}$

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$\bold { \red {(a+b)^2 = a^2 + 2ab + b^2 } }$

$\bold { \red {(a-b)^2 = a^2 - 2ab + b^2 } }$

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

$\bold { \red {(a-b)^3 = a^3 -b^3 - 3ab(a-b) } }$

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$\underline{\boxed{\bold{Given}}}$

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$\longrightarrow ( x - \dfrac{1}{x}) = 3$

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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Let's use last identity to solve this question :

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$\boxed{\bold { \orange {:\leadsto\; (x-\frac{1}{x} )^3 = x^3 -\frac{1}{3^3} - [3.x.\frac{1}{x} ](x-\frac{1}{x} ) } }}$

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$\bold { {:\implies \; (x-\frac{1}{x} )^3 = x^3 -\frac{1}{x^3} - 3(x-\frac{1}{x} ) } }$

$\bold { {:\implies \; (3 )^3 = x^3 -\frac{1}{x^3} - 3(3) } }$

$\bold { {:\implies \; 27 = x^3 -\frac{1}{x^3} - 9 } }$

$\bold { {:\implies \; x^3 -\frac{1}{x^3} = 27+ 9 } }$

$\bold { \pink {:\implies \; x^3 -\frac{1}{x^3} = 36 } }$

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$\boxed{\boxed{\bold{\therefore Value \; of \;  x^3 -\frac{1}{x^3} = 36 }}}$

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Hope this helps u.../

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