Question

Please give me Answe this question​

Answer 1

Step-by-step explanation:

x + 1/x = 4

x + 1/x = 4 ---( 1 )

Do the square of equation ( 1 ),

( x + 1/x )² = 4²

x² + 1/x² + 2 = 16

x² + 1/x² = 16 - 2

x² + 1/x² = 14 --( 2 )

Again do the square of equation ( 2 ),

( x² + 1/x² )² = 14²

x⁴ + 1/x⁴ + 2 = 196

x⁴ + 1/x⁴ = 196 - 2

= 194

Answer 2

Question :

If x + $\dfrac{1}{x}$ = 4. Then find x⁴ + $\dfrac{1}{{x}^{4}}$

Solution :

=> x + $\dfrac{1}{x}$ = 4

Squaring on both sides

=> $\bigg(x \: + \: \dfrac{1}{x}\bigg) \: = \: (4)^{2}$

(a + b)² = a² + b² + 2ab

=> ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: + \: 2 \bigg(x \: \times \: \dfrac{1}{x }\bigg) \: = \: 16$

=> ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: + 2\: = \: 16$

=> ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: = \: 16 \: - \: 2$

=> ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: = \: 14$ _________ (eq 1)

Again squaring on both sides

=> $\bigg( {x}^{2} \: + \: \dfrac{1}{ {x}^{2} }\bigg)^{2} \: = \: (14)^{2}$

=> ${x}^{4} \: + \: \dfrac{1}{ {x}^{4} } \: + \: 2 \: = \: 196$

=> ${x}^{4} \: + \: \dfrac{1}{ {x}^{4} } \: = \: 196 \: - \: 2$

=> ${x}^{4} \: + \: \dfrac{1}{ {x}^{4} } \: = \: 194$

_____________________________

${x}^{4} \: + \: \dfrac{1}{ {x}^{4} } \: = \: 194$

___________ [ ANSWER ]

____________________________