Question

plz answer this question with step by step explaination​

Answer 1

Answer:

$x ^{3} + \frac{1}{x ^{3} } = 18$

Step by step explanation:

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

To find:

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

Solution:

$(x + \frac{1}{x} ) ^{2} = x ^{2} + \frac{1}{x^{2} } + 2 \times x \times \frac{1}{x} \\ put \: value \: ofx ^{2} + \frac{1}{x ^{2} } in \: above \: equation \\ (x + \frac{1}{x} )^{2} = 7 + 2 \\ (x + \frac{1}{x} ) ^{2} = 9 \\ (x + \frac{1}{x} ) ^{2} = (3) ^{2} \\ taking \: square \: of \: both \: side \\ x + \frac{1}{x} = 3$

Now,

$cubic \: both \: side \\ (x + \frac{1}{x} ) ^{3} = (3) ^{3} \\ x ^{3} + \frac{1}{x ^{3} } + 3x( \frac{1}{x} )(x + \frac{1}{x} ) = 27 \\ x ^{3} + \frac{1}{x ^{3} } + 3(x + \frac{1}{x} ) = 27 \\put \: value \: of \: (x + \frac{1}{x})in \: above \: equation \\ x ^{3} + \frac{1}{x ^{3} } +3 \times 3 = 27 \\ x ^{3} + \frac{1}{x ^{3} } + 9 = 27 \\ x ^{3} + \frac{1}{x ^{3} } = 27 - 9 \\ x ^{3} + \frac{1}{x ^{3} } = 18$

Hope this answer help you