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The sum of two numbers is 6 times their ...

The sum of two numbers is 6 times their geometric means, show that numbers are in the ratio `(3+2sqrt(2)):(3-2sqrt(2))`.

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The sum of two numbers is 6 times their geometric mean, show that the numbers are in the ratio (3 + 2sqrt(2)) : (3 - 2sqrt(2))

If the A.M. of two numbers is twice their G.M., show that the numbers are in the ratio (2+sqrt(3)):(2-sqrt(3)).

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

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

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))

If the A.M. and G.M. between two numbers are in the ratio x:y , then prove that the numbers are in the ratio (x+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2))) .

If the A.M. of two positive numbers aa n db(a > b) is twice their geometric mean. Prove that : a : b=(2+sqrt(3)):(2-sqrt(3))dot

If the A.M. of two positive numbers aa n db(a > b) is twice their geometric mean. Prove that : a : b=(2+sqrt(3)):(2-sqrt(3))dot

Show that the following numbers are irrational. (i) 6+sqrt(2) (ii) 3-sqrt(5)

If three unequel numbers are in HP and their squares are in AP, show that they are in the ratio 1+sqrt(3):-2:1-sqrt(3) " or " 1-sqrt(3):-2:1+sqrt(3) .

RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Find the two numbers whose A.M. is 25 and GM is 20.

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

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

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

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

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

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

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  9. If the sum of an infinite decreasing G.P. is 3 and the sum of the squa...

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  10. If p^(th), q^(th) and r^(th) terms of G.P. are x,y,z respectively then...

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  11. If A1 and A2 are two A.M.s between a and b and G1 and G2 are two G.M.s...

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  12. If second, third and sixth terms of an A.P. are consecutive terms of a...

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

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  14. If n geometric means are inserted between two quantities ; then the pr...

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  15. If a=1+b+b^2+b^3+...... to\ oo , then write b in terms of a given that...

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  16. If in an infinite G.P., first term is equal to 10 times the sum of all...

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  17. If the first term of a G.P. a1, a2, a3, ddot is unity such that 4a2+5...

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  18. If a ,b ,c ,d are in A.P. and x , y , z are in G.P., then show that x^...

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  19. The first three of four given numbers are in G.P. and their last three...

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  20. If S be the sum P the product and R be the sum of the reciprocals of n...

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