[Toán 8] Bài tập về tính GTBT?

T

tomboy1442001

Từ điều kiện \Rightarrow $xy + yz + xz = 0$

\Rightarrow $xy = - yz - xz$

\Rightarrow $yz = - xy - xz$

\Rightarrow $xz = - xy - yz$

Ta có: $x^2 + 2yz = x^2 + yz + yz = x^2 + yz - xy - xz = (x-y)(x-z)$
$y^2 + 2xz = y^2 + xz + xz = y^2 + xz - xy - yz = (y-z)(y-x)$
$z^2 + 2xy = z^2 + xy + xy = z^2 + xy - yz - xz = (z-x)(z-y)$

Suy ra :

$A = \frac{yz}{x^2 +2yz} + \frac{xz}{y^2 + 2xz} + \frac{xy}{x^2 + 2xy}$

$= \frac{yz}{(x-y)(x-z)} + \frac{xz}{(y-z)(y-x)} + \frac{xy}{(z-x)(z-y)}$

$= - \frac{xy(x-y) + yz(y-z) + xz(x-z)}{(x-y)(y-z)(x-z)}$

$= \frac{(x-y)(y-z)(x-z)}{(x-y)(y-z)(x-z)}$

$= 1$
 
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