Math, asked by amareshmadhuri, 10 months ago

please give me answer by step by step formula​

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Answers

Answered by Anonymous
1

Have a look on the attachment

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Answered by BrainlyPopularman
5

QUESTION :

 \\ \:  \sf \: { \huge{.}}  \:  \: if \:\:  {x}^{2}  +  \dfrac{1}{ {x}^{2}}  = 6 \: , \: find \:  \: the \:  \: value \:  \: of \:  \:  {x}^{4}  +  \dfrac{1}{ {x}^{4} }  \\

ANSWER :

 \\ \dashrightarrow  \:  \: { \sf {x}^{4}  +  \dfrac{1}{ {x}^{4} } = 34 } \\

EXPLANATION :

GIVEN :

 \\ \:  \sf \: { \huge{.}} \:\:  {x}^{2}  +  \dfrac{1}{ {x}^{2}}  = 6 \\

TO FIND :

 \\ \:  \sf \: { \huge{.}} \:\:Value \:  \: of \:  \:  {x}^{4}  +  \dfrac{1}{ {x}^{4} }=? \\

SOLUTION :

 \\ \sf \implies  {x}^{2}  +  \dfrac{1}{ {x}^{2}}  = 6 \\

• Square on both sides –

 \\ \sf \implies \left \{ {x}^{2}  +  \dfrac{1}{ {x}^{2}} \right \}^{2}  =  {(6)}^{2}  \\

• Using formula –

 \\ \sf \:  \dashrightarrow \:  \left \{ a + b \right \}^{2}  =  {a}^{2} +  {b}^{2} + 2ab \\

• So –

 \\ \sf \implies  {x}^{4}  +  \dfrac{1}{ {x}^{4} } + 2( {x}^{4}) \left( \dfrac{1}{ {x}^{4} }  \right) =  {(6)}^{2}  \\

 \\ \sf \implies  {x}^{4}  +  \dfrac{1}{ {x}^{4} } + 2 (  \cancel{{x}^{4}}) \left( \dfrac{1}{  \cancel{{x}^{4}} }  \right) = 36  \\

 \\ \sf \implies  {x}^{4}  +  \dfrac{1}{ {x}^{4} } + 2 = 36  \\

 \\ \sf \implies  {x}^{4}  +  \dfrac{1}{ {x}^{4} } = 36 - 2  \\

 \\ \implies {\boxed{ \sf {x}^{4}  +  \dfrac{1}{ {x}^{4} } = 34 }} \\

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