Question

if x+1/x=3 find x²+1/x² and x³+1/x³​

Answer 1

Answer:

$x + \frac{1}{x} = 3 - (i) \\ \blue{\mathfrak{\underline{\large{Square \: on \: both \: sides}}}:} \\ {(x + \frac{1}{x}) }^{2} = {(3)}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 3 \times x \times \frac{1}{x} = 9 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 3 = 9 \\ \boxed{{x}^{2} + \frac{1}{ {x}^{2} } = 6} - (ii) \\ {(x + \frac{1}{x} )}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times {x}^{2} \times \frac{1}{x} + 3 \times x \times \frac{1}{ {x}^{2} } \\ {(3)}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) \\ 27 = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 3 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 27 - 9 \\ \boxed{{x}^{3} + \frac{1}{ {x}^{3} } = 18} \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \blue{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$