Question

8rootx - 15rooty = - rootxy

10/rootx + 8/rooty = 4​

Answer 1

x = 25; y = 16

Step-by-step explanation:

Given

$8\sqrt{x}-15\sqrt{y}=-\sqrt{xy}$

or, $\frac{8\sqrt{x}}{\sqrt{x}\sqrt{y}}-\frac{15\sqrt{y}}{\sqrt{x}\sqrt{y}}=-1$

or, $\frac{8}{\sqrt{y}}-\frac{15}{\sqrt{x}}=-1$

or, $\frac{15}{\sqrt{x}}-\frac{8}{\sqrt{y}}=1$

Taking $\frac{1}{\sqrt{x}}=u$ and  $\frac{1}{\sqrt{x}}=v$

We get

$15u-8v=1$   ............. (1)

Similarly, the other equation i.e. $\frac{10}{\sqrt{x}}+\frac{8}{\sqrt{y}}=4$ can be written as

$10u+8v=4$  .............. (2)

Adding equation (1) and equation (2)

We get

$25u=5$

$\implies u=\frac{5}{25}=\frac{1}{5}$

$\implies \frac{1}{\sqrt{x}}=\frac{1}{5}$

$\implies \sqrt{x}=5$

$\implies x=5^2=25$

Putting the value of u in equation (2)

$10\times\frac{1}{5}+8v=4$

$\implies 8v=2$

$\implies v=\frac{2}{8}=\frac{1}{4}$

$\implies \frac{1}{\sqrt{y}}=\frac{1}{4}$

$\implies \sqrt{y}=4$

$\implies y=16$

Therefore, x = 25, y = 16

Hope this answer is helpful.

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