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[halosix]

Cho a, b, c khác nhau thỏa $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}$. Rút gọn $P=\frac{a^{2}}{a^{2}+2bc}+\frac{b^{2}}{b^{2}+2ac}+\frac{c^{2}}{c^{2}+2ab}$

Edited by hachinh2013, 22-02-2015 - 23:36.

[stupidgirl]

a,b,c khác nhau thỏa (a+b+c)^{2}=a^{2}+b^{2}+c^{2}. Rút gọn P=\frac{(a)^{2}}{a^{2}+2bc}+\frac{(b)^{2}}{b^{2}+2ac}+\frac{(c)^{2}}{c^{2}+2ab}

theo đề => $ab+bc+ca=0$ => $P=\frac{a^{2}}{a^{2}+bc-ab-ac}+\frac{b^{2}}{b^{2}+ac-ab-bc}+\frac{c^{2}}{c^{2}+ab-bc-ac}$

<=> $P=\frac{a^{2}}{(a-b)(a-c)}+\frac{b^{2}}{(b-c)(b-a)}+\frac{c^{2}}{(c-a)(c-b)}$

quy đồng rút gọn P=1