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The ratio of the.A.M. and G.M. of two po...

The ratio of the.A.M. and G.M. of two positive numbers a and b is m : n. Show that `a: b = (m + sqrt(m^(2)-n^(2))): (m- sqrt(m^(2)-n^(2)))`

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c r...

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  2. The sum of two numbers is 6 times their geometric mean, show that numb...

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  3. The ratio of the.A.M. and G.M. of two positive numbers a and b is m : ...

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  4. If G1 is the first of n geometric means between a and b, show that : G...

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  5. If G is the geometric mean between two distinct positive numbers a and...

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  6. If A.M. and G.M pf roots of a quadratic equation are 8 and 5 respectiv...

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

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

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

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

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

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

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

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

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

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

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

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

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

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