Question

if a,b,c are in gp and x,y, are the arithmetic means between a,b and b,c respectively , then a/x+c/y​

Answer 1

Answer:

I hope this is the correct answer

Answer 2

Concept Introduction:-

It may be in the form of a word, a symbol, or a figure that reflects the arithmetic value of a quantity.

Given Information:-

We have been given that $a,b,c$ are in gp and $x,y$, are the arithmetic means between a,b and b,c respectively

To Find:-

We have to find that $a/x+c/y$

Solution:-

According to the problem

Since $a,b,c$ are in GP

$b^2 = ac$

Since $x$ is the arithmetic mean between $a$ and $b$

$x = (a+b)/2$

Also $y = (b+c)/2$

$a/x + c/y = 2a/(a+b) + 2c/(b+c)\\= [2a(b+c) + 2c(a+b)]/(a+b)(b+c)\\= (2ab + 2ac+ 2ac + 2bc)/(ab + b^2 + ac + bc)\\= 2(ab + 2ac + bc)/(ab+ 2ac+ bc) ( since b^2 = ac)\\= 2$

Final Answer:-

The correct answer is $2$.

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