giai,cho,minh,bai,nay,di cho,a,b,c>=0.CMR:a^3+b^3+c^3>=3abc
cho a^3+b^3+c^3=3abc .cmr:a+b+c=0 hoặc a=b=c
bai nay kho qua cac ban giai minh jup.a) cho a,b,c thoa man a+b+c=0.chung minh rang a^3+b^3+c^3=3abc
b)cho x^3+y^3=1.tinh gia tri bieu thuc p=2x^6+3x^3y^3+y^3+y^6
cho a+b+c=0
cmr:a^3+b^3+c^3=3abc
Ta có :
Giả thuyết : a + b + c = 0
(a + b + c)3 = 0
a3 + b3 + c3 + 3.(a + b)(b + c)(c + a) = 0
Từ a + b + c = 0
=> \(\hept{\begin{cases}a+b=-c\\b+c=-a\\c+a=-b\end{cases}}\)
=> a3 + b3 + c3 + 3.(-c)(-a)(-b) = 0
=> a3 + b3 + c3 = 3abc
giai bai mau cho minh nha: x^2-8x+16=0 ; 4x^2+12x+9=0 ; a^3-b^3+c^+3abc ; ab+ac+b^2+2ab+c^2 ; 3x^2+2x-1
Mn giúp mk vs:
Cho a+b+c=0
CMR:a3+b3+c3-3abc=0
Ta có : \(a+b+c=0\Rightarrow-a-b=c\)
\(\Rightarrow a^3+b^3+c^3-3abc=a^3+b^3+\left(-a-b\right)^3-3abc\)
\(=a^3+b^3-a^3-3a^2b-3ab^2-b^3-3abc\)
\(\Rightarrow-3a^2b-3ab^2-3abc=3ab\left(-a-b\right)-3abc\)
\(=3abc-3abc=0\) (đpccm)
bài 1: CMR a,b,c>= 0 thì a3+b3+c3>=3abc
bài 2 CMR
Nếu a+b+c=0 thì (a2+b2+c2)2=2(a4+b4+c4)
cac ban oi giup minh di 2 bai nay kho wa minh lam k mai k ra. mong cac ban giup minh
bai 1. CMR \(\left(\frac{a+b+c}{3}\right)^3>=abc\) với a,b,c>0
cac ban giup minh giai ro cho minh di
choA+B+C=0 CMR:a^3+b^3+c^3=3abc cmr:a^2+b^2+c^2=2(a^4+b^4+c^4)
\(Cho\)\(:\)\(a+b+c=0\)
\(CMR:a^3+b^3+c^3=3abc\)
\(a+b+c=0\Rightarrow\left(a+b+c\right)^3=0\)
\(\left(a+b\right)^3+3c\left(a+b\right)\left(a+b+c\right)+c^3=0\)
\(a^3+b^3+3ab\left(a+b\right)+c^3=0\)
\(a^3+b^3+c^3+3ab\left(-c\right)=0\)
\(a^3+b^3+c^3=3abc\)
Ta có:\(a^3+b^3+c^3-3abc\)
\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\)
\(=\left[\left(a+b\right)^3+c^3\right]-\left[3ab\left(a+b\right)+3abc\right]\)
\(=\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+2ab-ac-bc+3c^2-3ab\right)\)
\(=0\left(a^2+b^2+c^2-ab-bc-ca\right)=0\)
\(\Leftrightarrow a^3+b^3+c^3-3abc=0\)
\(\Leftrightarrow a^3+b^3+c^3=3abc\left(dpcm\right)\)