Question

If x^a=y^b=(xy)^c show that ab=c (a+b)

Answer 1

Step-by-step explanation:

I hope it would help you

Answer 2

If x^a=y^b=(xy)^c, then ab=c (a+b).

Step-by-step explanation:

It is given that

$x^a=y^b=(xy)^c$

Let,

$x^a=y^b=(xy)^c=p$

On equating side with k we get

$x^a=p\Rightarrow x=p^{1/a}$           ... (1)

$y^b=p\Rightarrow y=p^{1/b}$           .... (2)

$(xy)^c=p\Rightarrow xy=p^{1/c}$                .... (3)

Substitute the values of x and y from equation (1) and (2).

$p^{1/a}p^{1/b}=p^{1/c}$

Using the properties of exponent we get

$p^{\frac{1}{a}+\frac{1}{b}}=p^{1/c}$

On comparing both sides we get

$\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{c}$

$\dfrac{a+b}{ab}=\dfrac{1}{c}$

On cross multiplication we get

$c(a+b)=ab$

Hence proved.

#Learn more

If a^x-1=bc, b^y-1=ca, c^z-1=ab, then show that xy+yz+zx=xyz.​

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