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If x=1-sqrt(2),find the value of (x-1/x)...

If `x=1-sqrt(2)`,find the value of `(x-1/x)^3`

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`1/x=1/(1-sqrt2)xx(1+sqrt2)/(1+sqrt2)`
`(1+sqrt2)/(1^2-sqrt2^2)`
`(1+sqrt2)/(1-2)`
`-1-sqrt2`
Using this formula
`(a+b)(a-b)=a^2-b^2`
`(x-1/x)^3=[1-sqrt2-(-1-sqrt2)]^3`
`[1-sqrt2+1+sqrt 2]^3`
`(2)^3`
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RD SHARMA-RATIONALISATION -All Questions
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  2. If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

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  3. If x=1-sqrt(2),find the value of (x-1/x)^3

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  4. If x=3-2sqrt(2),find x^2+1/(x^2)

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  5. If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^2-b...

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  6. If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt...

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  7. Show that: 1/(3-sqrt(8))-1/(sqrt(8)-sqrt(7))+1/(sqrt(7)-sqrt(6))-1/(sq...

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  8. Simplify each of the following :3/(5-sqrt(3))+2/(5+sqrt(3))

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  9. If x=2+sqrt(3) , find the value of x^2+1/(x^2)

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  10. Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+sqrt(4))+1/(...

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  11. Simplify : (5+sqrt(5))(5-sqrt(5)) (ii) (3+2sqrt(2))(3-2sqrt(2))

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  12. Simplify the following expressions: (3+sqrt(3))(2+sqrt(2))

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  13. Simplify the following: (16)^(1/5)xx(2)^(1/5)

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  14. Simplify the following expressions: (i)(11+sqrt(11))(11-sqrt(11)) ...

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  15. Simplify the following expressions: (4+sqrt(7))(3+sqrt(2))

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  16. Simplify each of the following: (i) 4 3×16 3 (ii) (1250 4)/(2 4)

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  17. Simplify : (sqrt(5)+sqrt(2))^2

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  18. Rationalise the denominator of 2/(sqrt(3)) .

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  19. Simplify the following expressions: (i)(sqrt(3)+sqrt(7))^2 (ii) ...

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  20. Simplify each of the following: (i) root(5)(16)xxroot(5)(2) (ii) ro...

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