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uproscic wyrazenie
: 04 lis 2010, 17:18
autor: syjam122
uproscic wyrazenie tego typu
\(\frac{x^2}{(x-y)(x-z)}+\frac{y^2}{(y-x)(y-z)}+\frac{z^2}{(z-x)(z-y)}\)
: 04 lis 2010, 17:57
autor: irena
\(\frac{^2}{(x-y)(x-z)}+\frac{y^2}{(y-x)(y-z)}+\frac{z^2}{(z-x)(z-y)}=\frac{x^2(y-z)-y^2(x-z)+z^2(x-y)}{(x-y)(x-z)(y-z)}=\\=\frac{x^2y-x^2z-xy^2+y^2z+xz^2-yz^2}{(x-y)(x-z)(y-z)}=\frac{xy(x-y)+z^2(x-y)-z(x^2-y^2)}{(x-y)(x-z)(y-z)}=\frac{(x-y)(xy+z^2-z(x+y))}{(x-y)(x-z)(y-z)}=\\=\frac{(x-y)(xy+z^2-xz-yz)}{(x-y)(x-z)(y-z)}=\frac{(x-y)(x(y-z)-z(y-z))}{(x-y)(x-z)(y-z)}=\frac{(x-y)(y-z)(x-z)}{(x-y)(x-z)(y-z)}=1\)
: 04 lis 2010, 18:04
autor: syjam122
dzieki serdeczne