Question

solve : X+y/xy=3/2 and x-y/xy=1/2​

Answer 1

Answer:

The solution is,

x = 2, y = 1

Step-by-step explanation:

Given equations,

$\frac{x+y}{xy}=\frac{3}{2}$, $\frac{x-y}{xy}=\frac{1}{2}$

In first equation,

$\frac{1}{y}+\frac{1}{x}=\frac{3}{2}$

$\implies \frac{2}{y}+\frac{2}{x}=3----(1)$

Similarly, In second equation,

$\frac{x-y}{xy}=\frac{1}{2}$

$\implies \frac{2}{y}-\frac{2}{x}=1----(2)$

Adding equation (1) and (2),

We get,

$\frac{4}{y}=4$

$\implies y = 1$

FRom equation (1),

$2+\frac{2}{x}=3$

$\frac{2}{x}=1$

$\implies x = 2$

Answer 2

Answer:

The value of x and y is 1 and 2 respectively.

Step-by-step explanation:

Given:

Solve: $\frac{X+y}{xy}=\frac{3}{2} and \frac{x-y}{xy}=\frac{1}{2}$

Solution:

$\frac{X+y}{xy}=\frac{3}{2} ..(1)$

Simplifying the equation we get,

$\frac{1}{y} + \frac{1}{x} = \frac{3}{2}, \frac{2}{y} + \frac{2}{x} = \frac{3}{2} ..(2)$

Similarly $\frac{x-y}{xy}=\frac{1}{2} ..(3)$

Simplifying we get  

$\frac{2}{y} - \frac{2}{x} = 1 ...(4)$

Simplifying (3) and (4),

Finally,

we get  

Y = 1, x = 2

Result:

1 and 2 is the value of X and Y respectively.

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