\(a+b+c=0\Rightarrow\left(a+b+c\right)^2=0\Rightarrow a^2+b^2+c^2=-2\left(ab+bc+ac\right)\)Mà \(ab+bc+ac=0\Rightarrow a^2+b^2+c^2=0\Rightarrow a=b=c=0\)

Vậy \(M=-2005^{2006}\)

\(P^2=\dfrac{\left(a-b\right)^2}{\left(a+b\right)^2}=\dfrac{a^2-2ab+b^2}{a^2+2ab+b^2}=\dfrac{3a^2+3b^2-6ab}{3a^2+3b^2+6ab}=\dfrac{4ab}{16ab}=\dfrac{1}{4}\Rightarrow P=\dfrac{1}{2}\)

4) Ta có : A=(a+b+c+d)(a-b-c+d)=(a-b+c-d)(a+b-c-d)

=> (a+d)² - (b+c)²= (a-d)² - (c-b)²

=> a²+ d²+ 2ad - b²- c²- 2bc=a² + d² - 2ad - c²-b²+2bc

Rút gọn ta được: 4ad = 4bc => ad = bc =>\(\dfrac{a}{c}=\dfrac{b}{d}\)

16 gói keo to nặng 16.125=2000g

15 gói keo nho nang 15.80=1200g

so gam keo cua hang da ban 2000+1200=3200g=3.2kg

1) a²+b²+c²+3=2(a+b+c) =>(a-1)²+(b-1)²+(c-1)²=0

=> a-1=b-1=c-1=0 => a=b=c=1 =>đpcm