\(A=4\cdot3\left(-2\right)-2\left(3+2\right)=-24-10=-34\\ B=\left(x+y\right)^2-3\left(x+y\right)=\left(x+y\right)\left(x+y-3\right)=\left(x+y\right)\left(2+1-3\right)=0\)

a: \(\left(x+2\right)^2+\left(x+8\right)\left(x+2\right)=0\)

=>(x+2)(x+2+x+8)=0

=>(x+2)(2x+10)=0

=>(x+2)(x+5)=0

=>\(\left[\begin{array}{l}x+2=0\\ x+5=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-2\\ x=-5\end{array}\right.\)

b: \(B=\left(x+y\right)\left(x^2-xy+y^2\right)-y^3\)

\(=x^3+y^3-y^3=x^3\)

Khi x=10 thì \(B=10^3=1000\)

a: \(M=(x−y)(x2−xy)−x(x2+2y2)M=(x−y)(x2−xy)−x(x2+2y2)\)

\(=x3−x2y−x2y+xy2−x3−2xy2=x3−x2y−x2y+xy2−x3−2xy2\)

\(=−2x2y−xy2=−2x2y−xy2\)

Khi x=2 và y=-3 thì \(M=−2⋅22⋅(−3)−2⋅(−3)2M=−2⋅22⋅(−3)−2⋅(−3)2\)

\(=−8⋅(−3)−2⋅9=24−18=6=−8⋅(−3)−2⋅9=24−18=6\)

b: \(N=x(x2+xy+y2)−y(x2+xy+y2)N=x(x2+xy+y2)−y(x2+xy+y2)\)

\(=(x2+xy+y2)(x−y)=x3−y3=(x2+xy+y2)(x−y)=x3−y3\)

Khi x=4 và y=-1 thì \(N=43−(−1)3=64+1=65N=43−(−1)3=64+1=65\)

c: \(P=a2(a+b)−b(a2−b2)+2013P=a2(a+b)−b(a2−b2)+2013\)

\(=a2(a+b)−b(a−b)(a+b)+2013=a2(a+b)−b(a−b)(a+b)+2013\)

\(=(a+b)(a2−ba+b2)+2013=a3+b3+2013=(a+b)(a2−ba+b2)+2013=a3+b3+2013\)

Khi a=1 và b=-1 thì \(P=13+(−1)3+2013=2013P=13+(−1)3+2013=2013\)

Lời giải:

$x^2+y^2=(x+y)^2-2xy=4-2(-35)=74$

\(x=\dfrac{1}{y}\Rightarrow\dfrac{1}{y}-y=4\\ \Rightarrow y^2+4y-1=0\\ \Leftrightarrow\left[{}\begin{matrix}y=-2-\sqrt{5}\Rightarrow x=2-\sqrt{5}\\y=-2+\sqrt{5}\Rightarrow x=2+\sqrt{5}\end{matrix}\right.\)

Với \(x=2-\sqrt{5};y=-2-\sqrt{5}\)

\(A=x^2+y^2=18\\ B=x^3-y^3=76\\ C=x^4+y^2=322\)

Với \(x=2+\sqrt{5};y=-2+\sqrt{5}\)

\(A=x^2+y^2=18\\ B=x^3-y^3=76\\ C=x^4+y^4=322\)

A=x^2+y^2

=(x-y)^2+2xy

=4^2+2=18

B=(x-y)^3+3xy(x-y)

=4^3+3*1*4

=64+12=76

C=(x^2+y^2)^2-2x^2y^2

=18^2-2

=322

lấy máy tính thay số vào rồi tính thôi

A=xy(x+y)-x^2(x+y)+y^2(x+y)

=(x+y)(xy-x^2+y^2)

=x^3+y^3

Thay vào rồi tính típ nha.

B=(2x-1)(2x-1-3+2x)

=(2x-1)(4x-4)

Thay vào rồi tính típ.