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If x = (5-sqrt(3))/(5+sqrt(3)) and y = ...

If `x = (5-sqrt(3))/(5+sqrt(3)) and y = (5+sqrt(3))/(5-sqrt(3))`, show that `x -y = - (10sqrt(3))/(11)`

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RS AGGARWAL-NUMBER SYSTEMS-Exercise 1F
  1. Simplify by raationalising the denominator. (i) (7sqrt(3) - 5sqrt(2...

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  2. Simplify (2+ sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))

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  3. Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+...

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  4. Find the value of a and b if (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/...

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  5. Simplify (sqrt(13)-sqrt(11))/(sqrt(13)+sqrt(11)) + (sqrt(13)+sqrt(11))...

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  6. If x=3+2sqrt(2), check whether x+1/x is rational or irrational.

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

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  8. If x = 9 - 4sqrt(5), find the value of x^(2) +(1)/(x^(2)).

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  9. If x = (5-sqrt(21))/2, find the value of x+(1)/(x)

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  10. If a=3-2sqrt2, find the value of a^2-1/a^2.

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  11. If x = sqrt(13)+2sqrt(3), find the value of x-(1)/(x) .

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

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  13. If x = (5-sqrt(3))/(5+sqrt(3)) and y = (5+sqrt(3))/(5-sqrt(3)), show ...

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  14. If a= (sqrt(5) + sqrt(2))/(sqrt(5) -sqrt(2)) and b = (sqrt(5)-sqrt(2))...

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  15. If a=(sqrt3-sqrt2)/(sqrt3+sqrt2) and b=(sqrt3+sqrt2)/(sqrt3-sqrt2) the...

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  16. If p = (3-sqrt(5))/(3+sqrt(5)) and q = (3+sqrt5)/(3-sqrt(5)),find the...

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  17. Rationalise the denominator of each of the following. (i) (1)/(sqr...

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  18. Given, sqrt2 = 1.414 and sqrt6=2.449, find the value of 1/(sqrt3-sqrt2...

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  19. If x=1/(2-sqrt(3)), find the value of x^3-2x^2-7x+5

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  20. Evaluate 15/( sqrt10+sqrt20+sqrt40-sqrt5-sqrt80) is being given that s...

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