Question

2) If (x+1/x) = 3, find the value of i) (x^2+1/x^2) ii) (x^4+1/x^4)​

Answer 1

Answer:

i) answer is 7

ii) answer is 47

Answer 2

Answer:

$x^{2} + \frac{1}{x^{2} }= 7$

$x^{4} + \frac{1}{x^{4}}= 47$

Step-by-step explanation:

$x + \frac{1}{x} = 3$

i) $x^{2} + \frac{1}{x^{2} }$

$(x + \frac{1}{x} )^{2} = (3)^{2}$                                              $(a + b)^{2} = a^{2} + b^{2} + 2ab$

$x^{2} + \frac{1}{x^{2}} + 2(x)(\frac{1}{x}) = 9$

$x^{2} + \frac{1}{x^{2} }+ 2= 9$

$x^{2} + \frac{1}{x^{2} } = 9 - 2$

$x^{2} + \frac{1}{x^{2} }= 7$

ii)$x^{4} + \frac{1}{x^{4} }$

$(x^{2} + \frac{1}{x^{2} } )^{2} = (7)^{2}$                                                $(a + b)^{2} = a^{2} + b^{2} + 2ab$

$x^{4} + \frac{1}{x^{4}} + 2(x^{2} )(\frac{1}{x^{2} }) = 49$

$x^{4} + \frac{1}{x^{4}} + 2= 49$

$x^{4} + \frac{1}{x^{4}}= 49 - 2$

$x^{4} + \frac{1}{x^{4}}= 47$