Question

If x2 + 1/x2 = 6 then find x ^4 + 1/x^4 ​

Answer 1

Step-by-step explanation:

help full for you......

Answer 2

${ \bf{ \underline{ \blue{ \underline{ \blue{ Given}}}} : - }}$

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

${ \bf{ \underline{ \blue{ \underline{ \blue{ To -Find}}}} : - }}$

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

$\sf\blue{Formula \ to \ be \ used:-}$

• ( a + b)² = a² + b² + 2ab

${ \bf{ \underline{ \blue{ \underline{ \blue{ Solution }}}} : - }}$

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

( Squaring on both sides)

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

Here,

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

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

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

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

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

$\small{\underline{\sf{\blue{Hence-}}}}$

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

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Some more identities :-

•x² – y²= (x – y) (x + y)

•(x +y)² = a² + 2xy + y²

•x² + y² = (x + y)² – 2xy

•(x – y)² = x² – 2xy + y²

•(x + y + z)²

= x² + y² + z² + 2xy + 2yz + 2zx

•(x – y – z)²

= x² + y² + z² – 2xy + 2yz – 2zx

•(x + y)³ = x³ + 3x²y + 3xy² + y³