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

1.	If x² + 1/x² = 38, find the value of: x4 + 1/x4.
Answer» 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 – $\\ \implies \bf {({x}^{2})}^{2} + \bigg(\dfrac{1}{ {x}^{2} } \bigg)^{2} + 2( {x}^{2})\bigg(\dfrac{1}{ {x}^{2} } \bigg)=1444 \\$ $\\ \implies \bf {x}^{4} +\dfrac{1}{ {x}^{4} }+ 2 \cancel{( {x}^{2})}\bigg(\dfrac{1}{ \cancel{ {x}^{2} }} \bigg)=1444 \\$ $\\ \implies \bf {x}^{4} +\dfrac{1}{ {x}^{4} }+ 2=1444 \\$ $\\ \implies \bf {x}^{4} +\dfrac{1}{ {x}^{4} }=1444 - 2 \\$ $\\ \implies \large \red { \boxed{\bf {x}^{4} +\dfrac{1}{ {x}^{4} }=1442 }}\\$

Answer»

GIVEN :–

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