Question

If x² + 1/x² = 38, find the value of: x4 + 1/x4.​

Answer 1

Answer:

thanks and I also give the explanation of formula which I used

Answer 2

GIVEN :–

$\\ \implies \bf {x}^{2} + \dfrac{1}{ {x}^{2} } = 38$

TO FIND :–

$\\ \implies \bf {x}^{4} + \dfrac{1}{ {x}^{4} } =?$

SOLUTION :–

$\\ \implies \bf {x}^{2} + \dfrac{1}{ {x}^{2} } = 38$

• Square on both sides –

$\\ \implies \bf \bigg({x}^{2} + \dfrac{1}{ {x}^{2} } \bigg)^{2} =(38)^{2}$

$\\ \implies \bf \bigg({x}^{2} + \dfrac{1}{ {x}^{2} } \bigg)^{2} =1444$

• Using identity –

$\\ \implies \large\pink{ \boxed{\bf (a + b)^{2} = {a}^{2} + {b}^{2} + 2ab}}$

• So that –

$\\ \implies \bf {({x}^{2})}^{2} + \bigg(\dfrac{1}{ {x}^{2} } \bigg)^{2} + 2( {x}^{2})\bigg(\dfrac{1}{ {x}^{2} } \bigg)=1444$

$\\ \implies \bf {x}^{4} +\dfrac{1}{ {x}^{4} }+ 2 \cancel{( {x}^{2})}\bigg(\dfrac{1}{ \cancel{ {x}^{2} }} \bigg)=1444$

$\\ \implies \bf {x}^{4} +\dfrac{1}{ {x}^{4} }+ 2=1444$

$\\ \implies \bf {x}^{4} +\dfrac{1}{ {x}^{4} }=1444 - 2$

$\\ \implies \large \red { \boxed{\bf {x}^{4} +\dfrac{1}{ {x}^{4} }=1442 }}$