Question

8 root x minus 15 root Y equal to minus root xy and 10 by root x + 8 by root y is equal to 4 what is value of x and y ... please respond before 12 pm Tomorrow my kind request please​

Answer 1

Answer:

The value of x is 25.

The value of y is 16.

Step-by-step-explanation:

NOTE: Kindly refer to the attachment first.

The given equations are

$\sf\:8\:\sqrt{x}\:-\:15\:\sqrt{y}\:=\:-\:\sqrt{xy}\:\:\:-\:-\:-\:(\:1\:)\\\\\frac{10}{\sqrt{x}}\:+\:\frac{8}{\sqrt{y}}\:=\:4\:\:\:-\:-\:-\:(\:2\:)\\\\\implies\sf\:\frac{10\sqrt{y}\:+\:8\sqrt{x}}{\sqrt{xy}}\:=\:4\\\\\implies\sf\:10\:\sqrt{y}\:+\:8\:\sqrt{x}\:=\:4\:\sqrt{xy}\\\\\implies\sf\:8\:\sqrt{x}\:+\:10\:\sqrt{y}\:=\:4\:\sqrt{xy}\:\:\:-\:-\:-\:(\:3\:)$

Now, by subtracting equation ( 3 ) from equation ( 1 ), we get,

$\sf\:\cancel{8\:\sqrt{x}}\:+\:15\:\sqrt{y}\:=\:-\sqrt{xy}\:\:\:-\:\:-\:(\:1\:)\\\\\sf\:-\:\cancel{8\:\sqrt{x}}\:+\:10\:\sqrt{y}\:=\:4\:\sqrt{xy}\:\:-\:-\:(\:3\:)\\\\\sf\:25\:\sqrt{y}\:=\:5\:\sqrt{xy}\\\\\sf\:Now,\\\\\sf\:25\:\sqrt{y}\:=\:5\:\sqrt{xy}\\\\\implies\sf\:25\:\sqrt{y}\:=\:5\:\sqrt{x}.\sqrt{y}\\\\\implies\sf\:\frac{\cancel25}{\cancel5}\:=\:\frac{\sqrt{x}.\cancel{\sqrt{y}}}{\cancel{\sqrt{y}}}\\\\\implies\sf\:5\:=\:\sqrt{x}\\\\\implies\sf\:\sqrt{x}\:=\:5\:\:-\:-\:-\:(\:4\:)$

Now, by putting $\sf\:\sqrt{x}\:=\:5$ in equation ( 3 ), we get,

$\sf\:8\:\sqrt{x}\:+\:10\:\sqrt{y}\:=\:4\:\sqrt{xy}\:\:-\:-\:-\:(\:3\:)\\\\\implies\sf\:8\:\times\:5\:+\:10\:\sqrt{y}\:=\:4\:\sqrt{x}.\sqrt{y}\\\\\implies\sf\:40\:+\:10\:\sqrt{y}\:=\:4\:\times\:5\:\sqrt{y}\\\\\implies\sf\:40\:+\:10\:\sqrt{y}\:=\:20\:\sqrt{y}\\\\\implies\sf\:40\:=\:20\:\sqrt{y}\:-\:10\:\sqrt{y}\\\\\implies\sf\:40\:=\:10\:\sqrt{y}\\\\\implies\sf\:\sqrt{y}\:=\:\frac{\cancel40}{\cancel10}\\\\\implies\sf\:\sqrt{y}\:=\:4\:\:\:-\:-\:-\:(\:5\:)$

Now, by taking square of both sides in equations ( 4 ) & ( 5 ), we get,

$\sf\:(\:\sqrt{x}\:)^{2}\:=\:(\:5\:)^{2}\\\\\implies \boxed{\red{\sf\:x\:=\:25}}\\\\\sf\:And,\\\\\sf\:(\:\sqrt{y}\:)^{2}\:=\:(\:4\:)^{2}\\\\\implies \boxed{\red{\sf\:y\:=\:16}}$

Verification:

By substituting the values of x and y in LHS of equation ( 1 ), we get,

$\sf\:8\:\sqrt{x}\:-\:15\:\sqrt{y}\\\\\implies\sf\:8\:\sqrt{25}\:-\:15\:\sqrt{16}\\\\\implies\sf\:8\:\times\:5\:-\:15\:\times\:4\\\\\implies\sf\:40\:-\:60\\\\\implies\sf\:-20$

Now, by substituting the values of x and y in RHS of equation ( 1 ), we get,

$\sf\:-\:\sqrt{xy}\\\\\implies\sf\:-\:\sqrt{25\:\times\:16}\\\\\implies\sf\:-\:(\:5\:\times\:4\:)\\\\\implies\sf\:- \: 20$

$\therefore\large\boxed{\red{\sf\:LHS\:=\:RHS}}$

Hence verified!

Answer 2

Answer:

Thanks apke answer ke liye .

where are you from?