Các câu hỏi tương tự
Cho a. b, c > 0 . Chung minh rang : 4/a + 5/b + 3/c >= 4(3/a+b + 2/b+c + 1/c+a)
chung minh a^4 +b^4 +c^4=2(ab+bc+ac)^2 biet rang a+b+c=0
cho a,b,c la 3 so duong, chung minh:
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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
chung minh rang
(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(c+a)
cho a,b,c la 3 canh cua tam giac chung minh A = 2a^2b^2+2b^2c^2+2c^2a^2-a^4-b^4-c^4
Cho a+b+c=0.Chung minh rang
a4+b4+c4 = 2.(a2b2+b2c2+c2a2) = 2.(ab+bc+ca)2 = \(\frac{\left(a^2+b^2+c^2\right)^2}{2}\)
cho a;b;c la cac so nguyen , biet a+b+c chia het cho 6 chung minh rang a^3+b^3+c^3 chia het cho 6
Cho a + b + c = 3. Chứng minh rằng \(a^4+b^4+c^4\ge a^3+b^3+c^3\)
cho a^2+b^2+(a-b)^2=c^2+d^2+(c-d)^2.chung minh a^4+b^4+(a-b)^4=c^4+d^4+(c-d)^4