If- x-1y - 1 and y-1z - 1- then the value of xyz is

The correct option is A 1 Suppose Given equation x + 1y = 1 y 1z = 1 From the the 1st equation we have xy + 1 = y Substitute value of ...

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Standard VII

Mathematics

Equation

If, x+1y = ...

Question

If, $x + \frac{1}{y} = 1$ and $y - \frac{1}{z} = 1$ , then the value of $x y z$ is

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Solution

The correct option is A $1$
Suppose Given equation
$x + \frac{1}{y} = 1$
$y - \frac{1}{z} = 1$
From the the 1st equation we have

$x y + 1 = y$
Substitute value of $y$ in second equation we have:
$x y + 1 - \frac{1}{z} = 1$
$\Rightarrow x y z + z - 1 = z$
$\Rightarrow x y z + z - z = 1$
$\Rightarrow x y z = 1$
Hence, option 'A' is correct.

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If, x+1y=1 and y−1z=1, then the value of xyz is

The correct option is A 1Suppose Given equationx+1y=1y−1z=1From the the 1st equation we havexy+1=ySubstitute value of y in second equation we have:xy+1−1z=1⇒xyz+z−1=z⇒xyz+z−z=1⇒xyz=1Hence, option 'A' is correct.

If, $x + \frac{1}{y} = 1$ and $y - \frac{1}{z} = 1$ , then the value of $x y z$ is