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If a ,b ,c are in G.P. then prove that (...

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

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As `a,b,c` are in GP .
Note:
1. In general, the GP series is like `a,ar,ar^2…. `
2. In this, `b = ar` and `c = br = ar^2`
...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  2. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

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  7. The sum of three numbers a ,b ,c in A.P. is 18 . If a and b are each i...

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

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

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

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

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

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

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

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

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

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

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  20. Find four numbers in G.P. whose sum is 85 and product is 4096.

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