\(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ca=\)

\(=\left(a^2+b^2+c^2\right)+2\left(ab+bc+ca\right)=13^2=169\)

\(\Rightarrow85+2\left(ab+bc+ca\right)=169\Rightarrow ab+bc+ca=42\)

(a +b+c)² = a² + b² + c² + 2ab + 2ac + 2bc ( hằng đẳng thức mở rộng )

13² = 85 + 2 ( ab + bc +ca )

\(\Rightarrow\)ab + bc + ca = (169 - 85) :2 = 42

cam on

a, a+b+c=13

(a+b+c)²=169

a²+b²+c²+2ab+2bc+2ca=169

85+2(ab+bc+ac)=169

2(ab+bc+ac)=84

ab+ac+bc=42

2 câu cuối nhác nghĩ thông cảm cho mik nha

B) 9x^2 - 4y^2= (3x)^2-(2y)^2=(3x-2y)(3x+2y)=85(3x+2y)

Ta có : (a + b + c)² = a² + b² + c² + ab + bc + ca

13² = 85 + ab + bc + ca

ab + bc + ca = 169 - 85 = 84

(a+b+c)² = a² + b² + c² + 2(ab +bc +ac)

ab+bc+ac = 84/2 =42

P/s : a 2 = b 3 = c 8 là a/2=b/3=c/8

\(M=a^2+b^2+c^2-ab-bc-ca\)

\(=a\left(a-b\right)+b\left(b-c\right)+c\left(c-a\right)=2010a+2011b-4021c\)

\(=2010\left(a-c\right)+2011\left(b-c\right)=4021.2010+2011.2011\)

c - a ?

giải thích giúp mình với

 \(M=a^2+b^2+c^2-ab-bc-ca\)

\(M=a\left(a-b\right)+b\left(b-c\right)-c\left(a-c\right)\)

Ta có: \(a-b=2010\Leftrightarrow a=2010+b\)

         \(b-c=2011\Leftrightarrow c=b-2011\)

Suy ra \(a-c=2010+b-b+2011=4021\)

Thay vào \(M=\left(2010+b\right).2010+2011b-\left(b-2011\right).4021\)

                \(M=12126331\)