\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\Leftrightarrow\frac{ab+bc+ca}{abc}=0\Leftrightarrow ab+bc+ca=0\)
\(\left(a+b+c\right)^2=1\Leftrightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=1\Leftrightarrow a^2+b^2+c^2+2.0=1\)
=> dpcm
cho a+b+c=1 va 1/a+1/b+1/c=0.Chung minh rang : a^2+b^2+c^2=0
a+b+c=0 va 1/a+1/b+1/c=1 chung minh a^2+b^2+c^2=1
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
cho 3 so a,b,c khac 0 va (a+b+c)^2=a^2+b^2+c^2 . chung minh \(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}=3abc\)
Cho a;b;c>0
va ab+ac+bc=3
chung minh:\(\frac{1}{^a^{^2}+b^2+1}+\frac{1}{b^2+c^2+1}+\frac{1}{c^2+a^2+1}\le1\)
co ai hoc gioi toan 8 ko minh hoi 1 bai toan thui
Ch tam giac ABC(AB=AC) ve cac duong p giac BD va CE
a/Chung minh BE=Ce
b/chung minh ED//BC
c/Biet AB=AC=6cm,BC=4cm Tinh AD,DC,ED
a) a/b + b/a >_ 2
b) (a+b)(1/a +1/b)>_ 4
c) (a+b+c) (1/a +1/b +1/c)>_9
2. chung minh rang moi a, b la cac so tuy y, ta co :
a) (a-1)(a-3)(a-4)(a-6) +9 >_ 0
b) 4a(a-b)(a+1)(a+b+1) + b2 >_ 0
3. giai phuong trinh | x2 - x + 2| - 3x + 7 = 0
Cho a + b + c = 1 va a2 + b2 + c2 = 1. Neu \(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\)
Chung minh: xy + yz + xz = 0
