Question

answer for this question

Answer 1

x = 2+√3

1/x = 1/2+√3

Rationalise the denominator,

→ 1/(2+√3)×(2-√3)/(2-√3)

→ 2-√3/(2+√3)(2-√3)

→ 2-√3/(2²-√3²)

→ 2-√3/(4-3)

→ 2-√3/1

→ 1/x = 2-√3

According to the question, we need to find (x-1/x)³

→ {2+√3-(2-√3)}³

→ (2+√3-2+√3)³

→ {2√3)³

→ 2√3×2√3×2√3

→ 4(3)×2√3

→ 12×2√3

→ 24√3

Hope it helps

Answer 2

Hello friend

x=2+√3

1/x=1/(2+√3)

Rationalising the denominator we get

=2-√3/(2+√3)(2-√3)

=2-√3/2²-√3²

=2-√3/4-3

=2-√3/1

=2-√3

(x-1/x)³=(2+√3-(2-√3))³

=(2+√3-2+√3)³

=(2√3)³

=8×3√3

=24√3

Hope it helps