Question

a^x=b^y=c^2 and b^2 = ac prove that y = 2x2/x+2​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

GIVEN THAT,

b²=ac ---(1)

Also,

 $a^{x}=b^{y}=c^{z}$

let,

$a^{x}=b^{y}=c^{z}=p$

we have,

$a^{x}=p$

⇒$a= p^{ \frac{1}{x}}$

similarly,

$b=p^{\frac{1}{y}}$ and $c=p^{\frac{1}{z}}$

Putting value of a, b and c in eq(1)

We get,

$(p^{\frac{1}{y}})^{2}=p^{\frac{1}{x}}$×$p^{\frac{x}{y}}$

On equating the power of p

We get,

$\frac{2}{y}=\frac{1}{x}+\frac{1}{z}\\\frac{2}{y}=\frac{z+x}{xz} \\y=\frac{2xz}{z+x}$

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