chung minh rang ( a^2+b^2)(x^2+y^2) lon hon hoac bang (ax+by)^2
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Những câu hỏi liên quan
cho a la mot so nguyen .Chung to rang :a2 lon hon hoac bang 0;-a2 be hon hoac bang 0
chung minh rang (a+b+1)(a^2+b^2) +4/(a+b) lon hon hoac bang 8 voi ab=1 va a,b duong
cho ham so \(y=f\left(x\right)=ax^2+bx+c\)(a;b;c thuoc Q)
chung to rang f(-2)*f(3) nho hon hoac bang 0, biet rang 13a+b+2c=0
Ta có: \(f\left(x\right)=ax^2+bx+c\)
\(\Rightarrow f\left(-2\right)=4a-2b+c\)
\(f\left(3\right)=9a+3b+c\)
\(\Rightarrow f\left(-2\right)+f\left(3\right)=13a+b+2c=0\)(vì 13a+b+2c=0)
\(\Rightarrow f\left(-2\right)=-f\left(3\right)\)
\(\Rightarrow f\left(-2\right).f\left(3\right)=-\left[f\left(-2\right)\right]^2\le0\)( đpcm)
cho x+y =2. chung minh rang x^2015+y^2015 ba hon hoac bang x^2016+y^2016
Chung minh rang l x l lon hon hoac bang 0
nếu:\(|x|=0\Rightarrow x=0\)
\(|x|>0\Rightarrow x>0\)
vây \(|x|\ge0\)
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cho 2 diem B va C thuoc doan thang AD, M la 1 diem thuoc mat phang chung ming rang MA + MD lon hon hoac bang MB + MC
chung mnh rang:x^2+xy+y^2-3x-3y+3 lon hon hoac bang 0
cho ba so duong 0 nho hon hoac bang a nho hon hoac hoa bang b nho hon hoac bang c nho hon hoac bang 1 . chung minh a/bc+1+b/ac+1+c/ab+1nho hon hoac bang 2
chung minh rang : -3x^2+6x-y^2+6y-12 nho hon hoac bang 0
(cac ban giai nhanh nhe 5 like , minh dang can gap)
-3x2 + 6x -y2 +6y -12
<=> (-3x2 +6x -3) +( -y2 + 6y - 9)
<=> -3(x2 -2x +1) - (y2 -6y +9)
<=> -3(x-1)2 - (y-3)2
mà -3(x-1)2>=0
-(y-3)2>=0
=> dpcm
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= -3(x^2-2x+1)-(y^2-6y+9)
=-3(x-2)^2-(y-3)^2 nhỏ hơn hoặc bằng 0
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