Question

${\sf{x - \frac{1}{x} = 3 + 2 \sqrt{2} \: \: find \: {x}^{3} - \frac{1}{ {x}^{3} } }}$
Please don't spam. ​

Answer 1

Answer:

90 + 80√2

Step-by-step explanation:

Given,

x - 1/x = 3 + 2√2

Cubing both sides,

(x - 1/x)³ = (3 + 2√2)³

As, (a - b)³ = a³ - b³ - 3ab(a - b), so

x³ - 1/x³ - 3 × x × 1/x (x - 1/x) = 3³ + (2√2)³ +3(3)(2√2)(3+2√2)

x³ - 1/x³ - 3(x - 1/x) = 27 + 32√2 + 18 √2(3 + 2√2)

As , x-1/x = 3 + 2√2,

Thus, x³ - 1/x³ - 3(3 + 2√2) = 27 + 32√2 + 54√2 + 72

x³- 1/x³ = 99 + 86√2 - 9 - 6√2

THUS, x³-1/x³ = 90 + 80√2

$\huge\color{black}\boxed{\colorbox{turquoise}{\color{white}{Thanks}}}$

Answer 2

Answer

next step

final =90+64√2

common -3(x-1/x)

because x-1/x=3+2√2

I hope it helps you

nice question

solution=>