e a,e moi lop 5 thui

e có chs face k

Từ \(a^2+b^2+c^2=\frac{b^2-c^2}{a^2+3}+\frac{c^2-a^2}{b^2+4}+\frac{a^2-b^2}{c^2+5}\)

Ta có: \(\frac{a^2c^2+4a^2+b^2}{c^2+5}+\frac{a^2b^2+2b^2+c^2}{a^2+3}+\frac{b^2c^2+3c^2+a^2}{b^2+4}=0\)

\(\Rightarrow a=b=c=0\)

\(\Rightarrow2012ab+2013c=0\)

A= 1/3+1/6+...+1/300

1/2 x A = 1/2 x (1/3+1/6+...+1/300)

A/2 = 1/6+1/12+..+1/600

A/2 = 1/(2x3) + 1/(3x4) +....+ 1/ (24x25)

A/2 = 1/2-1/3+1/3-1/4+....+1/24-1/25

A/2 = 1/2 - 1/25

A/2 = 23/50

A = 23/25

vậy...

\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-a\right)\left(b-c\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}=2013\)

<=>\(\frac{\left(b-a\right)-\left(c-a\right)}{\left(a-b\right)\left(a-c\right)}+\frac{\left(c-b\right)-\left(a-b\right)}{\left(b-c\right)\left(b-a\right)}+\frac{\left(a-c\right)-\left(b-c\right)}{\left(c-a\right)\left(c-b\right)}=2013\)

<=>\(\frac{1}{c-a}+\frac{1}{a-b}+\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{b-c}+\frac{1}{c-a}=2013\)

<=>\(2\left(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\right)=2013\)

<=>\(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}=\frac{2013}{2}=1006,5\)

Ta có \(\left(\sqrt{x}-\sqrt{y}\right)^2\ge0\)\(\Rightarrow x-2\sqrt{xy}+y\ge0\)\(\Rightarrow x+y\ge2\sqrt{xy}\)

Mà x + y = 2 \(\Rightarrow\)\(2\ge2\sqrt{xy}\)\(\Rightarrow1\sqrt{xy}\le1\)\(\Rightarrow xy\le1\)

 Vi 2 = 2 + 0 ; 1 + 1 .nen x.y = 2 . 0 ; 1.1 chi bang 0 hoac 1 nen x.y <= 1

a: Xét ΔABM có 

AC là đường trung tuyến

AC=MB/2

Do đó: ΔABM vuông tại A

b: Xét ΔMCN và ΔNAP có 

MC=NA

\(\widehat{MCN}=\widehat{NAP}\)

CN=AP

Do đó:ΔMCN=ΔNAP

Suy ra: MN=NP

Cm tương tự, ta được: ΔNAP=ΔPBM

Suy ra: NP=PM

hay MN=NP=PM

=>ΔMNP đều

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