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If 2x = sqrt((a)/(b)) - sqrt((b)/(a)), t...

If `2x = sqrt((a)/(b)) - sqrt((b)/(a))`, then show that `(2a sqrt(1 + x^(2)))/(x + sqrt(1 + x^(2))) = a + b`

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CALCUTTA BOOK HOUSE-QUADRATIC SURDS-Exercise -3.2
  1. The value of sqrt(2+sqrt(2+ sqrt(2….oo))) is

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  2. If x + 7 + 4 sqrt3, then sqrtx + (1)/(sqrtx) = 4

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  3. root(5)((32)/(243)) is a surd

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  4. show that (7)/(2^((1)/(2)) + 2^((1)/(4)) + 1) = 1 - 3.2^((1)/(4)) + 2....

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  5. Write which one is a rational number and which one is a surd : root(6)...

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  6. Express as like surds: root(6)(5), root(5)(6)

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  7. Express as complete surds: 3 sqrt2, 2 root(3)(4)

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  8. (a) If x gt a, y gt b and x + y = a + b, then find which one of (sqrtx...

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  9. If x and y are rational and if x (3 + 2 sqrt2) - y sqrt2 = y(5 -3 sqrt...

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  10. Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)), (b) ...

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  11. Evaluate: (a) sqrt((x^(3))sqrt( y sqrt(x^(3)sqrt(y....oo)))) ,

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  12. If 2x = a + sqrt((4b^(3) - a^(3))/(3a)) and 2y = a - sqrt((4b^(3) - a^...

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  13. If (sqrt(a + 2b) + sqrt(a - 2b))/(sqrt(a + 2b) - sqrt(a - 2b)) = sqrt3...

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  14. If x^((1)/(3)) + y^((1)/(3)) + z^((1)/(3)) = 0, then prove that (x + y...

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  15. If y - mx = sqrt(a^(2) m^(2) + b^(2)) and x + my = sqrt(a^(2) + b^(2) ...

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  16. If 2x = a + (1)/(a) and 2y = b + (1)/(b), then prove that xy + sqrt((x...

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  17. If 2x = sqrt((a)/(b)) - sqrt((b)/(a)), then show that (2a sqrt(1 + x^(...

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  18. If x = [-(q)/(2) + sqrt((q^(2))/(4) + (p^(3))/(27))]^((1)/(3)) + [-(q)...

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  19. If n is a positive integer and U(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n...

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  20. If x = a^((1)/(3)) b^((1)/(3)) + a^(-(1)/(3)) + a^(-(1)/(3)) b^((1)/(3...

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