Question

Срочно, помогите!!!! Баллы!!!

Answer 1

Ответ:

$1)\ \ x^2+5x+6=(x+3)(x+2)\\\\\\x^2-10x+21=(x-3)(x-7)\\\\\\a^4-2a^3+a^2-1=(a^2-a)^2-1=(a^2-a-1)(a^2-a+1)\\\\\\x(x+4)-(y-2)(y+2)=x^2+4x-y^2+4=(x+2)^2-y^2=\\\\=(x+2-y)(x+2+y)\\\\\\a^3-b^3-3b^2-3b-1=a^3-(b+1)^3=(a-(b+1))(a^2+a(b+1)+(b+1)^2)=\\\\=(a-b-1)(a^2+ab+a+b^2+2b+1)$

$2)\ \ (2x+y)(2x+y-2)+1=(2x+y)^2-2(2x+y)+1=(2x+y-1)^2\\\\(2x+y-1)^2\geq 0\ \ \ dlya\ \ \forall x,y\in R$

$3)\ \ a+b+c=10\ \ ,\ \ a^2+b^2+c^2=60\\\\(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\ \ \ \Rightarrow \\\\100=60+2\, (ab+bc+ca)\\\\2(ab+bc+ca)=40\\\\ab+bc+ca=20$