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If A.M. and G.M. between two numbers is in the ratio `m : n` then prove that the numbers are in the ratio `(m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. If p^(t h),\ q^(t h),\ a n d\ r^(t h) terms of an A.P. and G.P. are bo...

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  2. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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  3. If A.M. and G.M. between two numbers is in the ratio m : n then prove...

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  4. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0and ...

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  5. Q. If a, b,c and d are distinct positive no. in AP. then (A) ad lt ...

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  6. Insert 6 geometric means between 27 and 1/(81)dot

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  7. Insert 5 geometric means between 16 and 1/4dot

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  8. Insert 5 geometric means between (32)/9a n d(81)/2dot

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  9. Find the geometric means of the following pairs of number: 2 and 8.

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  10. Find the geometric means of the following pairs of number: a^3b\ a n d...

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  11. Find the geometric means of the following pairs of number: -8\ a n d-2...

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  12. If a is the G.M. of 2\ a n d1/4, find adot

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  13. Find the two numbers whose A.M. is 25 and GM is 20.

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  14. If A and G are respectively arithmetic and geometric mean between posi...

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  15. The sum of two numbers is 6 times their geometric means, show that nu...

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  16. If A.M. and GM. of roots of a quadratic equation are 8 and 5, respe...

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  17. If AM and GM of two positive numbers a\ a n d\ b are 10 and 8 respecti...

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  18. If the fifth term of a G.P. is 2, then write the product of its 9 t...

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  19. If (p+q)^(t h)a n d\ (p-q)^(t h) terms of a G.P. re m\ a n d\ n respec...

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  20. If (log)x a ,\ a^(x//2) and (log)b x are in G.P., then write the value...

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