Question

xy/x+y=70 , xz/x+z=84 ,yz/y+z=140 find x , y and z​

Answer 1

Hello!

Answer:

x = 84

y = 420

z = infinity or 1/0

solution:

Refer the attachment plz...

Answer 2

Answer:

x = 105, y = 210, z = 420

Step-by-step explanation:

$i)\frac{xy}{x+y}=70$

$\implies \frac{x+y}{xy}=\frac{1}{70}$

$\implies \frac{1}{y}+\frac{1}{x}=\frac{1}{70}--(1)$

Similarly,

$\frac{1}{z}+\frac{1}{x}=\frac{1}{84}---(2)$

$\frac{1}{z}+\frac{1}{y}=\frac{1}{140}---(3)$

/* Add equations (1),(2)&(3), we get

$ii)2[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}]=\frac{1}{30}$

$\implies \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{60}---(4)$

/* subtract equation (1) from equation (4) , we get

$\frac{1}{z}=\frac{1}{420}$

$\implies z=420--(5)$

/* subtract equation (2) from equation (4) , we get

$\frac{1}{y}=\frac{1}{210}$

$\implies y=210--(6)$

/* subtract (3) from equation (4), we get

$\frac{1}{x}=\frac{1}{105}$

$\implies x=105--(7)$

Therefore,

x = 105, y = 210, z = 420

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