Các câu hỏi tương tự
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=1 va 1/a+1/b+1/c=0.Chung minh rang : a^2+b^2+c^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 a,b,c la 3 so duong, chung minh:
Xem chi tiết
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 khac 0 b khac 0 va a+b=1 chung minh rang \(\frac{b}{a^3-1}-\frac{a}{b^3-1}=\frac{2\left(a-b\right)}{a^2b^2+3}\)
1.tìm các nghiem nguyen cua phuong trinh: 54x^3+1=y^3
2.cho x+y=1 và xy khac 0.chung mih \(\frac{x}{y^3-1}+\frac{y}{x^3-1}+\frac{2\left(x-y\right)}{x^2y^2+3}=0\)
3.cho a,b,c la cac so thuc duong.chung minh :\(\left(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\right)^2+\frac{14abc}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\ge4\)
Cho a,b,c la so do 3 canh cua tam giac . Chung minh rang a2b+b2c+c2a+ca2+bc2+ab2-a3-b3-c3 > 0
Cho a/(b+c)+b/(c+a)+c/(a+b)=1. chung minh rang
a^2/(b+c)+b^2/(c+a)+c^2/(a+b)=0
a+b+c=0 va 1/a+1/b+1/c=1 chung minh a^2+b^2+c^2=1