\(a^2+b^2+1=a+b+ab\Leftrightarrow2a^2+2b^2+2=2a+2b+2ab\)
\(\Leftrightarrow\left(a^2-2ab+b^2\right)+\left(a^2-2a+1\right)+\left(b^2-2b+1\right)=0\)
\(\Leftrightarrow\left(a-b\right)^2+\left(a-1\right)^2+\left(b-1\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}a-b=0\\a-1=0\\b-1=0\end{cases}\Leftrightarrow}a=b=1\)
Cho a,b>0 VA a+b=1 chung minh rang (a+1/a)^2+(b+1/b)^2>/25/2
cho a = b + 1 chung minh (a + b)(a^2 + b^2)(a^4 + b^4)=a^8 - b^8
cho a-b=1 chung minh a^2+b^2>=1/2
cho a+b+c=1 va 1/a+1/b+1/c=0.Chung minh rang : a^2+b^2+c^2=0
cho a.b=1 chung minh rang (a^3+b^3)=(a^3+b^3)(a^2+b^2)-(a+b)
cho a+b+c=1 chung minh (a+bc)(b+ac)(c+ab)=(a+b)^2(a+c)^2(b+c)^2
cho a,b,c la 3 so khac 0 va a+b+c=0 chung minh rang 1/a^2+b^2-c^2+1/b^2+c^2-a^2+1/c^2+a^2-b^2=0
Cho a b c la cac so thuc. A+b+c=1 va 1/a+1/b+1/c=0. Chung minh A mu 2+ b mu 2+c mu 2=1
BAI 1: TIM X BIET so tu nhien x/7 du 6. chung minh rang x.x/7 du 1
bai 2: cho 2.(a.a+b.b)=(a+b).(a+b) chung minh rang a=b
