1/2.x- 2= 2.x+1
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a: \(A=\dfrac{x^2+2+x^2-1-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x}{x^2+x+1}\)
`@`Thay `x=2` vào `A` có:
`A=3^2-9.2=9-18=-9`
`@` Thay `x=1/3` vào `A` có:
`A=(1/3)^2-9. 1/3=1/9-3=-26/9`
Khi x=2 thì \(A=3\cdot2^2-9\cdot2=12-18=-6\)
Khi x=1/3 thì \(A=3\cdot\dfrac{1}{9}-9\cdot\dfrac{1}{3}=\dfrac{1}{3}-3=-\dfrac{8}{3}\)
\(Q=\left(\dfrac{1}{2\sqrt{x}+1}+\dfrac{1}{2\sqrt{x}-1}\right):\dfrac{1}{1-4x}\)
\(=\left(\dfrac{2\sqrt{x}-1}{\left(2\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}+\dfrac{2\sqrt{x}+1}{\left(2\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}\right).\left(1-4x\right)\)
\(=\left(\dfrac{2\sqrt{x}-1+2\sqrt{x}+1}{4x-1}\right)\left(1-4x\right)\)
\(=\dfrac{-4\sqrt{x}.\left(4x-1\right)}{4x-1}=-4\sqrt{x}\)
\(Q=\left(\dfrac{1}{2\sqrt{x}+1}+\dfrac{1}{2\sqrt{x}-1}\right):\dfrac{1}{1-4x}\left(dkxd:x\ge0;x\ne\dfrac{1}{4}\right)\)
\(=\left[\dfrac{2\sqrt{x}-1}{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}+\dfrac{2\sqrt{x}+1}{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}\right]\cdot\left(1-4x\right)\)
\(=\dfrac{2\sqrt{x}-1+2\sqrt{x}+1}{4x-1}\cdot\left[-\left(4x-1\right)\right]\)
\(=4\sqrt{x}\cdot\left(-1\right)\)
\(=-4\sqrt{x}\)
\(=\dfrac{x^3+x^2+x^2+x+x+1}{x^2+x}\)
\(=x+1+\dfrac{1}{x}\)
Ta có: x + y + 1 = 0
<=> x + y = -1
Thay x + y = -1 vào biểu thức N ta được:
N = x2(-1) - y2(-1) + x2 - y2 + 2(-1) + 3
N = -x2 + y2 + x2 - y2 - 2 + 3
N = (-x2 + x2) + (y2 - y2) + (-2 + 3)
N = -2+3=1
Vậy tại x+y+1=0 thì giá trị của biểu thức N là: 1.
\(x^3:\left(-\dfrac{1}{2}\right)^2=\dfrac{1}{2}\)
\(\Rightarrow x^3:\left(\dfrac{1}{2}\right)^2=\dfrac{1}{2}\)
\(\Rightarrow x^3=\left(\dfrac{1}{2}\right)^2\cdot\dfrac{1}{2}\)
\(\Rightarrow x^3=\left(\dfrac{1}{2}\right)^3\)
\(\Rightarrow x=\dfrac{1}{2}\)
\(x^3:\left(-\dfrac{1}{2}\right)^2=\dfrac{1}{2}\Rightarrow x^3=\dfrac{1}{2}.\left(-\dfrac{1}{2}\right)^2=\dfrac{1}{2}.\left(\dfrac{1}{2}\right)^2=\left(\dfrac{1}{2}\right)^3\)
\(\Rightarrow x=\dfrac{1}{2}\)
+ ĐK : \(x\ne-1\)
\(\frac{2x^2+2}{\left(x+1\right)^2}=\frac{\left(x^2+2x+1\right)+\left(x^2-2x+1\right)}{\left(x+1\right)^2}=\frac{\left(x+1\right)^2+\left(x-1\right)^2}{\left(x+1\right)^2}=1+\frac{\left(x-1\right)^2}{\left(x+1\right)^2}\ge1\forall x\ne-1\)
Dấu "=" xảy ra \(\Leftrightarrow\left(x-1\right)^2=0\Leftrightarrow x=1\)
Ta có : x2(x - 1) + (2x - 1)(x - a) = bx3 + cx2 + dx + 1
=> x3 + x2 - x + 2ax + a = bx3 + cx2 + dx + 1
=> x3 + x2 - x(2a - 1) + a = bx3 + cx2 + dx + 1
=> b = 1 ; c = 1 ; a = 1 ; 2a - 1 = d
=> b = 1 ; c = 1 ; a = 1 ; d = 1
Vậy a = b = c = d = 1
Tìm a,b,c,d chăng ??
Ta có: \(x^2\left(x-1\right)+\left(2x-1\right)\left(x-a\right)=bx^3+cx^2+dx+1\)
\(\Leftrightarrow x^3-x^2+2x^2-2ax-x+a=bx^3+cx^2+dx+1\)
\(\Leftrightarrow x^3+x^2-\left(2a+1\right)x+a=bx^3+cx^2+dx+1\)
Đồng nhất hệ số ta được:
\(\hept{\begin{cases}b=1\\c=1\\2a+1=-d\end{cases}}\) và \(a=1\)
=> \(\left(a;b;c;d\right)=\left(1;1;1;-3\right)\)
`1/2x-2 = 2x + 1`
`=> 2 . (1/2x - 2) = 2 . (2x + 1)`
`=> x - 4=4x+2`
`=> x - 4x = 2+4`
`=> -3x = 6`
`=> x=-2`
Vậy: `x=-2`