Question

answer question with photos​

Answer 1

PLZ MARK MY ANSWER AS BRAINLIEST ..☺️

Answer 2

Question: If x⁴ + 1/x⁴ = 119, find the value of x³ - 1/x³.

Answer:

$\large{\underline{\boxed{\sf x {}^{3} - \frac{1}{ {x}^{3} } = 36}}}$

Step-by-step explanation:

$\large{\underline{\underline{\sf Given \: that :}}}$

$\sf {x}^{4} + \frac{1}{ {x}^{4} } = 119 \\ \\ \bf adding \: 2 \: both \: sides - \\ \\ \sf ( {x}^{2} ) {}^{2} + (\frac{1}{ {x}^{2} } ) {}^{2} + 2 = 119 + 2 \\ \\ \sf (x {}^{2}) {}^{2} + (\frac{1}{x {}^{2} } ) {}^{2} + 2 \: . \: x {}^{2} \: . \: \frac{1}{x {}^{2} } = 121 \\ \\ \sf (x {}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = (11) {}^{2} \\ \\ \sf x {}^{2} + \frac{1}{x {}^{2} } = 11 \\ \\ \bf subtracting \: both \: sides - \\ \\ \sf x {}^{2} + \frac{1}{x {}^{2} } - 2 = 11 - 2 \\ \\ \sf x ^{2} + \frac{1}{ {x}^{2} } - 2 \: . \: x \: . \: \frac{1}{x} = 9 \\ \\ \sf (x - \frac{1}{x} ) {}^{2} = (3) {}^{2} \\ \\ \sf x - \frac{1}{x} = 3 \\ \\ \bf Now, on \: cubing \: both \: sides - \\ \\ \sf (x - \frac{1}{x}) {}^{3} = {(3)}^{3}$

[ ∵ (a - b)³ = a³ - b³ - 3ab (a - b)]

$\sf x {}^{3} - \frac{1}{ {x}^{3} } - 3 \: .\: x\:. \: \frac{1}{x} (x - \frac{1}{x} ) = 27 \\ \\ \sf x {}^{3} - \frac{1}{ {x}^{3} } - 3(3) = 27 \\ \\ \sf x {}^{3} - \frac{1}{ {x}^{3} } - 9 = 27 \\ \\ \sf x {}^{3} - \frac{1}{ {x}^{3} } = 27 + 9 \\ \\ \boxed{\bf x {}^{3} - \frac{1}{ {x}^{3} } = 36}$

Hence, the answer is 36.