Tính giá trị biểu thức

Question

Cho a+b+c=0. Tính giá trị biểu thức

$A= \frac{a^2}{cb} + \frac{b^2}{ca} + \frac{c^2}{ab}$

$B= \frac{a^2}{a^2 - b^2 - c^2} + \frac{b^2}{b^2 - c^2 - a^2 } + \frac{c^2}{c^2 - a^2 - b^2}$

phunsukwangdu98 · Answer 1 · 9/3/2014 8:26:19 PM

$\frac{a^2}{a^2 - b^2 - c^2} + \frac{b^2}{b^2 - c^2 - a^2 } + \frac{c^2}{c^2 - a^2 - b^2}$

phân số 1:$=\frac{a^2}{a^2-(b^2+c^2)}=\frac{a^2}{a^2-(a^2-2bc)}=\frac{a^2}{2bc}$

tương tự:$\frac{b^2}{b^2-c^2-a^2}=\frac{b^2}{2ac}$

$\frac{c^2}{c^2-a^2-b^2}=\frac{c^2}{2ab}$

$=>B=\frac{1}{2}A=\frac{3}{2}$

Trả lời 03-09-14 08:26 PM

phunsukwangdu98
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phunsukwangdu98 · Answer 2 · 9/3/2014 8:18:32 PM

a/$\frac{a^2}{cb} + \frac{b^2}{ca} + \frac{c^2}{ab}$

$=\frac{a^3+b^3}{abc}+\frac{c^2}{ab}$

$=\frac{(a+b)^3-3ab(a+b)}{abc}+\frac{c^2}{ab}$

$=\frac{-c^3+3abc}{abc}+\frac{c^2}{ab}$

$=3-\frac{c^2}{ab}+\frac{c^2}{ab}=3$

Trả lời 03-09-14 08:18 PM

phunsukwangdu98
241 1 5

106K 17K

3 1

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