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If a + (1)/(a)= p and a ne 0, then show ...

If `a + (1)/(a)= p and a ne 0`, then show that: `a^(3) + (1)/(a^(3))= p (p^(2)- 3)`

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ICSE-EXPANSIONS-Exercise 4(B)
  1. If a^(2) + (1)/(a^(2)) = 18 and a ne 0, find: a- (1)/(a)

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  2. If a^(2) + (1)/(a^(2)) = 18 and a ne 0, find: a^(3)- (1)/(a^(3))

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  3. If a + (1)/(a)= p and a ne 0, then show that: a^(3) + (1)/(a^(3))= p (...

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  4. If a + 2b= 5, then show that: a^(3) + 8b^(3) + 30ab = 125

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  5. If (a + (1)/(a))^(2) = 3 and a ne 0, then show that: a^(3) + (1)/(a^(3...

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  6. If a + 2b + c= 0, then show that: a^(3) + 8b^(3) + c^(3)= 6abc

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  7. Use property to evaluate: 13^(3) + (-8)^(3) + (-5)^(3)

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  8. Use property to evaluate: 7^(3) + 3^(3) + (-10)^(3)

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  9. Use property to evaluate: 9^(3) -5^(3) - 4^(3)

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  10. Use property to evaluate: 38^(3) + (-26)^(3) + (-12)^(3)

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  11. If a ne 0 and a - (1)/(a)= 3, find : a^(2) + (1)/(a^(2))

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  12. If a ne 0 and a - (1)/(a)= 3, find : a^(3)- (1)/(a^(3))

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  13. If a ne 0 and a - (1)/(a)= 4, find a^(2) + (1)/(a^(2))

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  14. If a ne 0 and a - (1)/(a)= 4, find a^(4) + (1)/(a^(4))

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  15. If a ne 0 and a - (1)/(a)= 4, find a^(3)- (1)/(a^(3))

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  16. If x ne 0 and x + (1)/(x) = 2, then show that: x^(2)+ (1)/(x^(2))= x^(...

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  17. If 2x- 3y= 10 and xy= 16, find the value of 8x^(3)- 27y^(3)

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  18. Expand: (3x+ 5y+ 2z) (3x- 5y + 2z)

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  19. Expand: (3x- 5y - 2z) (3x- 5y + 2z)

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  20. The sum of two numbers is 9 and their product is 20. Find the sum of t...

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