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If x ,y ,z are distinct positive numbers...

If `x ,y ,z` are distinct positive numbers, then prove that `(x+y)(y+z)(z+x)> 8x y zdot`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. If a is the A.M. of b and c and the two geometric means are G1 and G2...

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  2. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

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  3. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

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  4. If a ,b ,c are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+...

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  5. If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prov...

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  6. If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

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  7. If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) ar...

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  8. The sum of three numbers a ,b ,c in A.P. is 18 . If aa n db are eac...

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  9. If a ,b ,c are in G.P., prove that: a(b^2+c^2)=c(a^2+b^2)

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  10. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

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  11. If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db...

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  12. If x^a=x^(b//2)z^(b//2)=z^c , then prove that 1/a ,1/b ,1/c are in A.P...

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  13. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , t...

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  14. If the sum of three numbers in G.P. is 38 and their product is 1728, ...

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  15. If the p^(t h) and q^(t h) terms of a G.P. are q and p respectively, s...

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  16. In a finite G.P. the product of the terms equidistant from the begi...

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  17. The product of first three terms of a G.P. is 1000. If 6 added to its ...

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  18. Find three numbers in G.P. whose sum is 52 and the sum of whose pro...

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  19. Three numbers are in G.P. whose sum is 70. If the extremes be each ...

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  20. If the continued product of three numbers in G.P. is 216 and the sum o...

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