Question

Cho a,b,c khác 0; a²+2bc khác 0 ;b²+2ca khác 0; c²+2ab khác 0 và a²+b²+c²=(a+b+c)²

cmr : S=a²/a²+2bc + b²/b²+2ac + c²/c²+2ab =1

         M=bc/a²+2bc + ca/b²+2ac + ab/c²+2ab=1

giúp mk nha

mk cảm ơn nhiều

Answer 1

a²+b²+c²=(a+b+c)²<=> ab+bc+ca=0

\(\Rightarrow S=\frac{a^2}{a^2+bc-\left(ab+ca\right)}+\frac{b^2}{b^2+ac-\left(ab+bc\right)}+\frac{c^2}{c^2+ab-\left(bc+ca\right)}\)

\(=\frac{a^2}{\left(a-b\right)\left(a-c\right)}-\frac{b^2}{\left(b-c\right)\left(a-b\right)}-\frac{c^2}{\left(b-c\right)\left(c-a\right)}\)

\(=\frac{a^2\left(b-c\right)-b^2\left(a-c\right)-c^2\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=\frac{\left(a-b\right)\left(b-c\right)\left(c-a\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}=1\)

M  tương tự