Question

If x= 3-2√2. Find value of x^3-1/x^3

Answer 1

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Is in the attachment!!!

Answer 2

Answer:

x³-1/x^3

-140√2

Given X= 3-2√2 _____(1)

(1) 1/x = 1/3-2√2

Rationalising the denominator we get,

3+2√2/(3-2√2)(3+2√2)

3+2√2/3² - (2√2)^2

3+2√2/9-8

3+2√2 ________(2)

(2) x - 1/x

3 - 2√2 - (3+2√2)

3 - 2√2 - 3 - 2√2

-4√2__________(3)

Algebraic identity

a^3 - b^3 = (a + b)^3 + 3ab(a - b)

x^3 - 1/x^3

(x - 1/x)^3 + 3 × x × 1/x( x - 1/x)

(-4√2)^3 + 3(-4√2)

-128√2 - 12√2

-140√2

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hope it helps you.❤️

silentlover45.❤️