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\(A=\left(x+1\right)^3-\left(x+3\right)^2\left(x+1\right)+4x^2+8\)
\(A=\left(x^3+3x^2+3x+1\right)-\left(x^2+6x+9\right)\left(x+1\right)-4x^2+8\)
\(A=\left(x^3+3x^2+3x+1\right)-\left(x^3+x^2+6x^2+6x+9x+9\right)+4x^2+8\)
\(A=x^3+3x^2+3x+1-x^3-x^2-6x^2-6x-9x-9+4x^2+8\)
\(A=-12x\)
Thay \(x=-\dfrac{1}{6}\) vào \(A\) ta có:
\(A=-12\times\left(-\dfrac{1}{6}\right)=2\)
Vậy \(A=2\) khi \(x=-\dfrac{1}{6}\)
\(B=\left(x-1\right)^3-+\left(x+2\right)\left(x^2-2x+4\right)+3\left(x+4\right)\left(x-4\right)\)
\(B=\left(x^3-3x^2+3x-1\right)-\left(x^3-2x^2+4x+2x^2-4x+8\right)+\left(3x^2-48\right)\)
\(B=x^3-3x^2+3x-1-x^3+2x^2-4x-2x^2+4x-8+3x^2-48\)
\(B=3x-57\)
Thay \(x=-2\) vào \(B\) ta có:
\(B=3\times\left(-2\right)-57=-6-57=-63\)
Vậy \(B=-63\) khi \(x=-2\)
\(a,\dfrac{x-3}{4}+\dfrac{2x-1}{3}=-\dfrac{x}{6}\)
\(\Leftrightarrow\dfrac{3\left(x-3\right)+4\left(2x-1\right)+2x}{12}=0\)
\(\Leftrightarrow3x-9+8x-4+2x=0\)
\(\Leftrightarrow13x-13=0\)
\(\Leftrightarrow13x=13\)
\(\Leftrightarrow x=1\)
\(b,\left(x-3\right)\left(2x-1\right)=\left(2x-1\right)\left(2x+3\right)\)
\(\Leftrightarrow\left(x-3\right)\left(2x-1\right)-\left(2x-1\right)\left(2x+3\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x-3-2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\-x-6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-6\end{matrix}\right.\)
Tìm x
a) Ta có: \(3\left(1-4x\right)\left(x-1\right)+4\left(3x+2\right)\left(x+3\right)=38\)
\(\Leftrightarrow3\left(x-1-4x^2+4x\right)+4\left(3x^2+9x+2x+6\right)=38\)
\(\Leftrightarrow3\left(-4x^2+5x-1\right)+4\left(3x^2+11x+6\right)-38=0\)
\(\Leftrightarrow-12x^2+15x-3+12x^2+44x+24-38=0\)
\(\Leftrightarrow59x-17=0\)
\(\Leftrightarrow59x=17\)
hay \(x=\frac{17}{59}\)
Vậy: \(x=\frac{17}{59}\)
b) Ta có: \(5\left(2x+3\right)\left(x+2\right)-2\left(5x-4\right)\left(x-1\right)=75\)
\(\Leftrightarrow5\left(2x^2+4x+3x+6\right)-2\left(5x^2-5x-4x+4\right)-75=0\)
\(\Leftrightarrow5\left(2x^2+7x+6\right)-2\left(5x^2-9x+4\right)-75=0\)
\(\Leftrightarrow10x^2+35x+30-10x^2+18x-8-75=0\)
\(\Leftrightarrow53x-53=0\)
\(\Leftrightarrow53x=53\)
hay x=1
Vậy: x=1
c) Ta có: \(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)
\(\Leftrightarrow2x^2+3x^2-3=5x^2+5x\)
\(\Leftrightarrow5x^2-3-5x^2-5x=0\)
\(\Leftrightarrow-3-5x=0\)
\(\Leftrightarrow-5x=-3\)
hay \(x=\frac{3}{5}\)
Vậy: \(x=\frac{3}{5}\)
d) Ta có: \(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow8x+16-5x^2-10x+4\left(x^2+x-2x-2\right)+2\left(x^2-4\right)=0\)
\(\Leftrightarrow-5x^2-2x+16+4x^2-4x-8+2x^2-8=0\)
\(\Leftrightarrow x^2-6x=0\)
\(\Leftrightarrow x\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
Vậy: \(x\in\left\{0;6\right\}\)
bài 1 : điền vào chỗ chấm để đk khẳng định đúng :
a) (.x..+2y...)2=x2+..4y.+4y2
b) (.a..-.3b..)2=a2-6ab+.9b2..
c) (.m..+.\(\frac{1}{2}\)..)2=.m2..+m+1/4
d) 25a2-..\(\frac{1}{4}b\).=(.5a..+1/2b)(..5a..-1/2b)
e)(.2x...+.1..)^2 = 4x^2 +.4x..+1
g)(2-x)(.4..+.2x..+.x2..)=8-x^3
h) 16a^2 - ..9. = (..4a.+3)(..4a.-3)
f)25 - ..30y.+9y^2=(..5.+...3y.)^2