Question

Rationalise the denominator :-
[ Note - √3+2]

1. ( x+1/x )²
2.( x - 1/3 )²
3.( x³ - 1/x³ )
4.x³ - 1/x³
5.x² - 1/x²
6.√x + 1√3​

Answer 1

Answer:

2,4,11,13

hope this helpful

Answer 2

Given :- x = √3 + 2 .

Answer :-

→ x = √3 + 2

→ x = 2 + √3

→ 1/x = 1/(2 + √3) * {(2 - √3)/(2 - √3)} = (2 - √3)/(2)² - (√3)² = (2 - √3) / (4 - 3) = (2 - √3)

so,

→ x + 1/x = 2 + √3 + 2 - √3 = 4

→ (x + 1/x)² = 4² = 16 (Ans.)

and,

→ x - 1/x = 2 + √3 - (2 - √3) = w - 2 + √3 + √3 = 2√3

→ (x - 1/x)² = (2√3)² = 12 (Ans.)

also,

→ x² - 1/x² = (x + 1/x)(x - 1/x) = 4 * 2√3 = 8√3 (Ans.)

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