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2(a-b)(c-b)+2(b-a)(c-a)+2(b-c)(a-c)
=2a^2+2b^2+2c^2-2bc-2ab-2ac
=a^2-2ac+c^2+a^2-2ab+b^2+b^2-2bc+c^2
=(a-c)^2+(a-b)^2+(b-c)^2
1.
a. \(x^2-4x\Rightarrow x^2-4x+4=\left(x-2\right)^2\)
b. \(x^2+9\Rightarrow x^2+9+6x=\left(x+3\right)^2\)
c. \(x^2+xy+y^2\Rightarrow x^2+xy+y^2+xy=\left(x+y\right)^2\)
d. \(x^2-x\Rightarrow x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2\)
Ta có: (a+b+c)^2 + a^2 + b^2 + c^2
= a^2 +b^2 +c^2 + 2ab + 2ac + 2bc + a^2 + b^2 + c^2
= (a^2 +2ab+ b^2) + (b^2 +2bc+ c^2) +(c^2 +2ac+ a^2 )
= (a+b)^2 +(b+c)^2 +(c+a)^2
\(\left(a^2+b^2+c^2\right)+a^2+b^2+c^2\)
\(=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2\)
\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)
\(\left(a+b+c\right)^2+a^2+b^2+c^2\)
\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2\)
\(=a^2+2ab+b^2+b^2+2bc+c^2+c^2+2ca+a^2\)
\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)
a) (a + b + c)2 + a2 + b2 + c2
= a2 + b2 + c2 + 2ab + 2bc + 2ac +a2 + b2 + c2
= (a2 + 2ab + b2 ) + (b2 + 2bc + c2 ) + (a2 + 2ac + c2)
= (a + b)2 + (b + c)2 + (c+a)2
Bài 2:
a) \(B=x^2+x-11\)
\(=x^2+2.\frac{1}{2}.x+\frac{1}{4}-\frac{45}{4}\)
\(=\left(x+\frac{1}{2}\right)^2-\frac{45}{4}\ge-\frac{45}{4}\)
Dâu = xảy ra khi:
\(\left(x+\frac{1}{2}\right)^2=0\)
\(\Rightarrow x+\frac{1}{2}=0\)
\(\Rightarrow x=0-\frac{1}{2}=-\frac{1}{2}\)
b) \(C=x^2-8x+1\)
\(=x^2-2.4.x+16-15\)
\(=\left(x-4\right)^2-15\ge-15\)
Dấu = xảy ra khi:
\(\left(x-4\right)^2=0\)
\(\Rightarrow x-4=0\)
\(\Rightarrow x=0+4=4\)
Ko chắc à!
a,(a+b+c)^2+a^2+b^2+c^2
=a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+c^2
=(a^2+2ab+b^2)+(b^2+2bc+c^2)+(a^2+2ac+c^2)
=(a+b)^2+(b+c)^2+(a+c)^2
b,(2a-b)(c-b)+2(b-a)(c-a)+2(b-c)(a-c)
=2(a-b)(c-b-c+a)+2(b-c)(c-a)
=2(a-b)(a-b)+2(b-c)(c-a)
=2(a-b)^2+2(b-c)(c-a)
=2(a^2-2ab+b^2)+(ab-bc-ca+c^2)
=2(a^2+b^2+c^2-ab-bc-ca)
=(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)
=(a-b)^2+(b-c)^2+(c-a)^2
chúc bạn học tốt!!!
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