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If AM and GM of two positive numbers a a...

If AM and GM of two positive numbers `a and b` are 10 and 8 respectively, find the numbers.

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we have,
`(a+b)/2=10` and `sqrt(ab)=8=>a+b=20` and `ab=64`
Clearly,`a` and `b` are roots of the equation
`x^2-20x+64=0`
...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
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  2. If A and G are respectively arithmetic and geometric mean between posi...

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

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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 abs(b)...

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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, . . . is unity such that 4a2...

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

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