Question

if (x+1/x)=3 find (x³+1/x³)​

Answer 1

Question

if (x+1/x)=3 find (x³+1/x³)

Solution

$on \: cubing \: both \: sides \: \\ \\ ({x + \frac{1}{x} )}^{3} = {3}^{3} \\ \\ by \: using \: property \: of \: ({a + b})^{3} we \: get \:$

${x}^{3} + { \frac{1}{x} }^{3} + 3x \frac{1}{x} (x + \frac{1}{x} ) = 27 \\ \\{x}^{3} + { \frac{1}{x} }^{3} + 3(3) = 27 \: \: \: (coz \: x + \frac{1}{x} = 3) \\ \\ \\{x}^{3} + { \frac{1}{x} }^{3} + 9 = 27 \\ \\ {x}^{3} + { \frac{1}{x} }^{3} = 27 - 9 \\ \\ {x}^{3} + { \frac{1}{x} }^{3} = 18 \: \: \\ \\ \\ from \: above \: value \: of \: {x}^{3} + { \frac{1}{x} }^{3}is \: 18$

hope it helps

be brainly