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(1)
a) x=\(\dfrac{-1}{12}-\dfrac{2}{3}\)=\(\dfrac{-3}{4}\)
b) 2x+1=3 => 2x=3-1=2 => x=1
(2)
f(2)=2.22+4=12
f(-1)=2.(-1)2+4=6
(1)
a) \(x+\dfrac{2}{3}=-\dfrac{1}{12}\\ \Rightarrow x=-\dfrac{1}{12}-\dfrac{2}{3}\\ \Rightarrow x=\dfrac{-1}{12}-\dfrac{8}{12}\\ \Rightarrow x=-\dfrac{9}{12}=-\dfrac{3}{4}\)
Vậy \(x=-\dfrac{3}{4}\)
b) \(\left(2x+1\right)^2=9\\ \Rightarrow\left(2x+1\right)^2=3^2=\left(-3\right)^2\\ \Rightarrow\left[{}\begin{matrix}2x+1=3\\2x+1=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=2\\2x=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{-2;1\right\}\)
(2)
\(y=f\left(x\right)=2x^2+4\\ f\left(2\right)=2\cdot2^2+4=8+4=12\\ f\left(-1\right)=2\cdot\left(-1\right)^2+4=2+4=6\)
Vậy \(f\left(2\right)=12\\ f\left(-1\right)=6\)
a, P=-3(x^3.x)(y^2.y^3)
=-3x^4y^5
b, Thay x=-1 , y=2 vào đơn thức P . Ta có :
P=-3.(-1)^4.2^5
P=3.1.32
P=96
a)\(f\left(1\right)=2.1^2+5.1-3=2+5-3=4\)
\(f\left(0\right)=0+0-3=-3\)
\(f\left(1,5\right)=2.\left(1,5\right)^2-5.1,5-3=4,5-7,5-3=-6\)
a: \(A=\left(-1\right)^2\cdot2^3+\left(-1\right)\cdot2=8-2=6\)
b: \(B=2\cdot2^2+2^4+3\cdot2\cdot1-5=8+16+6-5=8+16+1=25\)
`a)`
`@f(1)=2.1^2+5.1-3=2.1+5-3=2+5-3=4`
`@f(0)=2.0^2+5.0-3=-3`
`@f(1,5)=2.(1,5)^2+5.1,5-3=4,5+7,5-3=9`
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`b)`
`***f(3)=9`
`=>3a-3=9`
`=>3a=12=>a=4`
`***f(5)=11`
`=>5a-3=11`
`=>5a=14=>a=14/5`
`***f(-1)=6`
`=>-a-3=6`
`=>-a=9=>a=-9`
a: f(1)=2+5-3=4
f(0)=-3
f(1,5)=4,5+7,5-3=9
b: f(3)=9 nên 3a-3=9
hay a=4
f(5)=11 nên 5a-3=11
hay a=14/5
f(-1)=6 nên -a-3=6
=>-a=9
hay a=-9
a) \(2x^2-3xy-2y^2=2\)
\(\Rightarrow2x^2+xy-4xy-2y^2=2\)
\(\Rightarrow x\left(2x+y\right)-2y\left(2x+y\right)=2\)
\(\Rightarrow\left(2x+y\right)\left(x-2y\right)=2\)
\(\Rightarrow\left(2x+y\right);\left(x-2y\right)\in\left\{-1;1;-2;2\right\}\)
Ta giải các hệ phương trình sau với x;y nguyên
1) \(\left\{{}\begin{matrix}2x+y=-1\\x-2y=-2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}4x+2y=-2\\x-2y=-2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}5x=-4\left(loại\right)\\x-2y=-1\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}2x+y=1\\x-2y=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}4x+2y=2\\x-2y=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}5x=4\left(loại\right)\\x-2y=-1\end{matrix}\right.\)
3) \(\left\{{}\begin{matrix}2x+y=-2\\x-2y=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}4x+2y=-4\\x-2y=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}5x=-5\\y=\dfrac{x+1}{2}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-1\\y=0\end{matrix}\right.\)
4) \(\left\{{}\begin{matrix}2x+y=2\\x-2y=1\end{matrix}\right.\) \(\left\{{}\begin{matrix}4x+2y=4\\x-2y=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}5x=5\\y=\dfrac{x+1}{2}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)
Vậy \(\left(x;y\right)\in\left\{\left(-1;0\right);\left(1;1\right)\right\}\)
b) \(xy-y+x=9\)
\(\Rightarrow y\left(x-1\right)+x-1+1=9\)
\(\Rightarrow\left(x-1\right)\left(y+1\right)=8\)
\(\Rightarrow\left(x-1\right);\left(y+1\right)\in\left\{-1;1;-2;2;-4;4;-8;8\right\}\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(0;-9\right);\left(2;7\right);\left(-1;-5\right);\left(3;3\right);\left(-3;-3\right);\left(5;1\right);\left(-7;-2\right);\left(9;0\right)\right\}\)
Thay `x = -1 ; y = 2` vào `A`, có:
`A = (-1)^2 . 2^3 + (-1) . 2`
`A = 1 . 8 - 1 . 2 = 6`
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Thay `x = 3 ; y = 2 ; z = 1` vào `B`. Ta có:
`B = 2 . 3^2 + 2^4 + 3 . 2 . 1 - 5`
`B = 2 . 9 + 16 + 6 - 5`
`B = 18 + 16 + 6 - 5 = 35`
Thay x=−1;y=2x=-1;y=2 vào A,
Ta có:A=(−1)2.23+(−1).2
A=(-1)2.23+(-1).2
A=1.8−1.2=6
A=1.8-1.2=6
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Thay x=3;y=2;z=1x=3;y=2;z=1 vào B.
Ta có:B=2.32+24+3.2.1−5
B=2.32+24+3.2.1-5
B=2.9+16+6−5B=2.9+16+6-5
B=18+16+6−5=35