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Question Number 112803 by Aina Samuel Temidayo last updated on 09/Sep/20

If x+y+z=0,   then the value of ((x^2 +y^2 +z^2 )/(x^2 −yz)) is

$$\mathrm{If}\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{0},\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} −\mathrm{yz}}\:\mathrm{is} \\ $$

Answered by MJS_new last updated on 09/Sep/20

z=−(x+y) ⇒ ((x^2 +y^2 +z^2 )/(x^2 −yz))=2

$${z}=−\left({x}+{y}\right)\:\Rightarrow\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{yz}}=\mathrm{2} \\ $$

Commented by Aina Samuel Temidayo last updated on 09/Sep/20

Solution?

$$\mathrm{Solution}? \\ $$

Commented by MJS_new last updated on 09/Sep/20

just insert and calculate

$$\mathrm{just}\:\mathrm{insert}\:\mathrm{and}\:\mathrm{calculate} \\ $$

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