Question

HEY GUYS ANYONE PLZ HELP ME❣️❣️❣️❣️

-> IF x-1/x = 3+2√2 , Find the value of x^3 + 1/x^3???

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Answer 1

Answer:

108 + 76√2

Step-by-step explanation:

It is given,

x - (1/x) = 3 + 2√2

Squaring both sides:

(x - 1/x)² = (3+ 2√2)²

=> x² + 1/x² - 2 = 9 + 8 + 12√2

⇒ x² + 1/x² = 19 + 12√2

We know that,

a³ - b³ = (a - b)(a² + b² + ab)

It means,

(x)³ - (1/x)³ = (x - 1/x)(x² + 1/x² +1)

=> (3 + 2√2)(19 + 12√2 + 1)

=> (3 +2√2)(20 +12√2)

=> (60+36√2+40√2+48)

=> 108 + 76√2

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Hope it helps!