Question

please please answer this question8 root x minus 15 root Y is equal to minus root x into Y and 10 by root x + 8 by root Y is equal to 4 find the value of x and y ​

Answer 1

Answer:

$x = 25 \text{ and } y = 16$

Step-by-step explanation:

$\text{Given linear equations are}$

$8\sqrt{x} - 15\sqrt{y} =-\sqrt{xy}$        ...(1)

$\cfrac{10}{\sqrt{x}} + \cfrac{8}{\sqrt{y}} = 4$                   ...(2)

$\text{Divide both sides of Eqn. (1) by } \sqrt{xy},$

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

$\Rightarrow \cfrac{8}{\sqrt{y}} - \cfrac{15}{\sqrt{x}} = -1$

$\Rightarrow -\cfrac{15}{\sqrt{x}} + \cfrac{8}{\sqrt{y}} = -1$        ...(3)

$\text{Now, let }\cfrac{1}{\sqrt{x}} = m \text{ and } \cfrac{1}{\sqrt{y}} = n$

$\text{So, Eqn. (3) becomes}$

$-15m + 8n = -1$                 ...(4)

$\text{And, Eqn. (2) becomes}$

$10m + 8n = 4$                ...(5)

$\text{Subtract Eqn. (5) from Eqn. (4),}$

$-15m + 8n -(10m + 8n) = -1 -4$

$\Rightarrow -15m + 8n - 10m - 8n = -5$

$\Rightarrow -25m = -5$

$\Rightarrow m = \cfrac{-5}{-25}$

$\Rightarrow m = \cfrac{1}{5}$

$\text{As, } \cfrac{1}{\sqrt{x}} = m$

$\therefore \cfrac{1}{\sqrt{x}} = \cfrac{1}{5}$

$\Rightarrow \sqrt{x} = 5$

$\Rightarrow x = (5)^2$

$\Rightarrow x = 25$

$\text{Put value of m in Eqn. (5),}$

$10\times\cfrac{1}{5} + 8 n = 4$

$\Rightarrow 2+8n = 4$

$\Rightarrow 8n = 4-2$

$\Rightarrow 8n = 2$

$\Rightarrow n = \cfrac{2}{8}$

$\Rightarrow n = \cfrac{1}{4}$

$\text{As, }\cfrac{1}{\sqrt{y}} = n$

$\therefore \cfrac{1}{\sqrt{y}} = \cfrac{1}{4}$

$\Rightarrow \sqrt{y} = 4$

$\Rightarrow y=4^2$

$\Rightarrow y = 16$

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