If X+Y+Z=15 and 1/x+1/y+1/z=0, then what is X^2+Y^2+Z^2?

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If X+Y+Z=15 and 1/x+1/y+1/z=0, then what is X^2+Y^2+Z^2?

$\frac{1}{X} + \frac{1}{Y} + \frac{1}{X} = 0$ $1/X+1/Y+1/X=0$

X+Y+Z=15

What is $X^{2} + Y^{2} + Z^{2}$ $X^2+Y^2+Z^2$ ?

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Answer 1 · 2017-04-29T10:56:19

$X^{2} + Y^{2} + Z^{2} = 225$ $X^2+Y^2+Z^2 =225$

Explanation:

$\frac{1}{X} + \frac{1}{Y} + \frac{1}{Z} = 0 or \frac{Y Z + Z X + X Y}{X Y Z} = 0 or (Y Z + Z X + X Y) = 0$ $1/X +1/Y+1/Z =0 or (YZ+ZX+XY)/(XYZ)=0 or (YZ+ZX+XY)=0$

${(X + Y + Z)}^{2} = X^{2} + Y^{2} + Z^{2} + 2 (X Y + Y Z + Z X)$ $(X+Y+Z)^2= X^2+Y^2+Z^2 + 2(XY+YZ+ZX)$ or
$15^{2} = X^{2} + Y^{2} + Z^{2} + 2 \cdot 0$ $15^2=X^2+Y^2+Z^2 + 2*0$ or
$X^{2} + Y^{2} + Z^{2} = 225$ $X^2+Y^2+Z^2 =225$ [Ans]

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If X+Y+Z=15 and 1/x+1/y+1/z=0, then what is X^2+Y^2+Z^2?

$\frac{1}{X} + \frac{1}{Y} + \frac{1}{X} = 0$ $1/X+1/Y+1/X=0$

X+Y+Z=15

What is $X^{2} + Y^{2} + Z^{2}$ $X^2+Y^2+Z^2$ ?

1 Answer

Explanation:

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If X+Y+Z=15 and 1/x+1/y+1/z=0, then what is X^2+Y^2+Z^2?

1X+1Y+1X=01/X+1/Y+1/X=0 X+Y+Z=15 What is X2+Y2+Z2X^2+Y^2+Z^2?

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Explanation:

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$\frac{1}{X} + \frac{1}{Y} + \frac{1}{X} = 0$ $1/X+1/Y+1/X=0$

X+Y+Z=15

What is $X^{2} + Y^{2} + Z^{2}$ $X^2+Y^2+Z^2$ ?