Math, asked by eshagajjar10, 10 months ago

if (x+1/x)=3 find (x³+1/x³)​

Answers

Answered by viperisbackagain
2

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

Similar questions