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a,
\(x^2+y^2=\left(x+y\right)^2-2xy=1^2-2\cdot\left(-6\right)=1-\left(-12\right)=13\)
\(x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=1\cdot\left[13-\left(-6\right)\right]=19\)
\(x^5+y^5=\left(x+y\right)\left(x^2+y^2\right)^2-\left(2x^3y^2+xy^4+x^4y+2x^2y^3\right)=169-\left[2\left(xy\right)^2\left(x+y\right)+xy\left(x^3+y^3\right)\right]=169-\left[2\cdot36\cdot1-6\cdot19\right]=211\)
1,Thực hiện phép tính :
a, (x + 2)9 : (x + 2)6
=(x+2)9-6
=(x+2)3
b, (x - y) 4 : (x - 2)3
=(x-y)4-3
=x-y
c, ( x2+ 2x + 4)5 : (x2 + 2x + 4)
=(x2+2x+4)5-1
=(x2+2x+4)4
d, 2(x2 + 1)3 : 1/3(x2 + 1)
=(2÷1/3).[(x2+1)3÷(x2+1)]
=6(x2+1)2
e, 5 (x - y)5 : 5/6 (x - y)2
=(5÷5/6).[(x-y)5÷(x-y)2]
=6(x-y))3
\(A=\left(x+y\right)^2-2xy=25-12=13\)
\(B=\left(x+y\right)\left(x^2+y^2-xy\right)=\left(x+y\right)\left[\left(x+y\right)^2-3xy\right]=5\left(25-18\right)=35\)
\(C=x^2-y^2\Rightarrow C^2=x^4+y^4-2x^2y^2=\left(x^2+y^2\right)^2-4x^2y^2\)
\(C^2=\left[\left(x+y\right)^2-2xy\right]^2-4\left(xy\right)^2=\left(25-12\right)^2-4.36=25\Rightarrow C=\pm5\)
\(D=\frac{x^2+y^2}{xy}=\frac{\left(x+y\right)^2-2xy}{xy}=\frac{25-12}{6}=\frac{13}{6}\)
Bài 1. Rút gọn:
\(a, x\left(1-x\right)+6\left(x+3\right)\left(x+3\right)\)
\(=x-x^2+6\left(x^2+6x+9\right)\)
\(=x-x^2+6x^2+36x+54\)
\(=5x^2+37x+54\)
\(b, \left(2-3x\right)\left(2+3x\right)-\left(x+5\right)\left(x-5\right)\)
\(=\left(4-9x^2\right)-\left(x^2-25\right)\)
\(=-10x^2+29\)
\(c, \left(3x+1\right)\left(x+5\right)-\left(x-1\right)\left(x+1\right)\)
\(=3x^2+15x+x+5-x^2+1\)
\(=2x^2+16x+6\)
\(d,\left(2-3x\right)\left(2x+3\right)+6\left(x-1\right)^2\)
\(=\left(4x+6-6x^2-9x\right)+6\left(x^2-2x+1\right)\)
\(=4x+6-6x^2-9x+6x^2-12x+6\)
\(=-17x+12\)
\(e, x\left(5-x\right)-\left(2x+2\right)\left(3x+2\right)-\left(x-2\right)\left(x+2\right)\)
\(=5x-x^2-\left(6x^2+4x+6x+4\right)-\left(x^2-4\right)\)
\(=5x-x^2-6x^2-4x-6x-4-x^2+4\)
\(=-8x^2-5x\)
Bài 2:
a: VT\(=x^3-xy+x^2y^2-y^3-x^3+y^3-x^2y^2\)
=-xy
b: \(VT=x^2+6xy+9y^2-x^2+9y^2-6xy=18y^2=VP\)
Ta có HPT:
\(\left\{{}\begin{matrix}x-y=5\\xy=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}xy-y^2=5y\\xy=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y^2=-6-5y\\xy=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-2\\x=3\end{matrix}\right.\)
Thay x = -2, y = 3 vào, ta được:
A = (-2)3 - 33 - (-2)2 + 2.(-2).3 - 32
A = -8 - 27 - 4 + (-12) - 9
A = -60
Sửa:
Ta có HPT:
\(\left\{{}\begin{matrix}x-y=-5\\xy=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}xy-y^2=-5y\\xy=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y^2=-6-\left(-5y\right)\\xy=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=-3\end{matrix}\right.\)
Thay x = -3, y = 2 vào, ta được:
A = (-3)3 - 23 - (-3)2 + 2.(-3).2 - 22
A = -27 - 8 - 9 + (-12) - 4
A = -60