Question

5. If X:Y:Z=4:3:2 and x^2+ y^2+ z^2 =11600, thenthe value of √X+Y-Z is equals toroot is on three of the​

Answer 1

Answer:

$\bf\sqrt{x+y-z}=10$

Step-by-step explanation:

Given:

$x:y:z=4:3:2$

Then

$x=4k,\:y=3k,\:z=2k$

Also

$x^2+ y^2+ z^2 =11600$

$\implies\;(4k)^2+ (3k)^2+(2k)^2 =11600$

$\implies\;16k^2+9k^2+4k^2 =11600$

$\implies\;29k^2 =11600$

$\implies\;k^2 =400$

$\implies\;k =20$

$\implies\\x=80\\y=60\\z=40$

Now,

$\sqrt{x+y-z}$

$=\sqrt{80+60-40}$

$=\sqrt{140-40}$

$=\sqrt{100}$

$=10$

$\implies\boxed{\bf\sqrt{x+y-z}=10}$