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If a is the A.M. of b and c and the two geometric means are `G_(1)` and `G_(2)`, then prove that `G_(1)^(3)+G_(2)^(3) = 2abc`

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If A.M. and G.M pf roots of a quadratic equation are 8 and 5 respectiv...

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  2. If one geometric mean G and two arithmetic means p amd q be inserted b...

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  3. If a is the A.M. of b and c and the two geometric means are G(1) and G...

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  4. If p ,q, r are in A.P., a is G.M. between p, q and b is G.M. between q...

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  5. Find n such that (a^n+b^n)/(a^(n-1)+b^(n-1)) may be the geometric mean...

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  6. If A and G be A.M. and G.M., respectively between two positive numbers...

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  7. If A and G are the A.M. and G.M. respectively between any two distinct...

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  8. The sum of first three terms of a G.P. is 39/10 and their product is 1...

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  9. The sum of first three terms of a GP. is 13/12 and their product is - ...

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  10. The sum of three numbers in A.P. is 15. If 1, 4 and 19 are added to th...

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  11. The sum of three numbers which are consecutive terms of an A.P. is 21....

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  12. There are four numbers such that the first three of them form an arith...

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  13. The sum of first three terms of a G.P. is 7 and the sum of their squar...

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  14. Find three numbers in G.P. : whose sum is 30 and whose Product is 216.

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  15. Find three numbers in G.P. : whose sum is 38 and whose product is 1728...

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  16. Find three numbers in G.P. whose sum is 35 and sum of their squares is...

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  17. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  18. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  19. If a, b,c are in G.P., prove that the following are also in G.P. : a...

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  20. If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G....

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