Tìm x biết
a, 3(1-4x)(x-1)+4(3x+2)(x+3)=38
b, 5(2x+3)(x+2)-2(5x-4)(x-1)=75
c, 2x^2+3(x-1)(x+1)=5x(x+1)
d, (8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0
Tìm x biết
a, 3(1-4x)(x-1)+4(3x+2)(x+3)=38
b, 5(2x+3)(x+2)-2(5x-4)(x-1)=75
c, 2x^2+3(x-1)(x+1)=5x(x+1)
d, (8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0
$\text{a) Ta có:}$ \(3\left(1-4x\right)\left(x-1\right)+4\left(3x+2\right)\left(x+3\right)=38\)
\(\Leftrightarrow3\left(x-1-4x^2+4x\right)+4\left(3x^2+9x+2x+6\right)=38\)
\(\Leftrightarrow3\left(-4x^2+5x-1\right)+4\left(3x^2+11x+6\right)-38=0\)
\(\Leftrightarrow-12x^2+15x-3+12x^2+44x+24-38=0\)
\(\Leftrightarrow59x-17=0\)
\(\Leftrightarrow59x=17\)
$\text{hay}$ \(x=\frac{17}{59}\)
$\text{Vậy:}$ \(x=\frac{17}{59}\)
$\text{b) Ta có:}$ \(5\left(2x+3\right)\left(x+2\right)-2\left(5x-4\right)\left(x-1\right)=75\)
\(\Leftrightarrow5\left(2x^2+4x+3x+6\right)-2\left(5x^2-5x-4x+4\right)-75=0\)
\(\Leftrightarrow5\left(2x^2+7x+6\right)-2\left(5x^2-9x+4\right)-75=0\)
\(\Leftrightarrow10x^2+35x+30-10x^2+18x-8-75=0\)
\(\Leftrightarrow53x-53=0\)
\(\Leftrightarrow53x=53\)
$\text{hay}$ $x=1$
$\text{Vậy:}$ $x=1$
$\text{c) Ta có:}$ \(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)
\(\Leftrightarrow2x^2+3x^2-3=5x^2+5x\)
\(\Leftrightarrow5x^2-3-5x^2-5x=0\)
\(\Leftrightarrow-3-5x=0\)
\(\Leftrightarrow-5x=-3\)
$\text{hay}$ \(x=\frac{3}{5}\)
$\text{Vậy:}$ \(x=\frac{3}{5}\)
$\text{d) Ta có:}$ \(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow8x+16-5x^2-10x+4\left(x^2+x-2x-2\right)+2\left(x^2-4\right)=0\)
\(\Leftrightarrow-5x^2-2x+16+4x^2-4x-8+2x^2-8=0\)
\(\Leftrightarrow x^2-6x=0\)
\(\Leftrightarrow x\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)
$\text{Vậy:}$ \(x\in\left\{0;6\right\}\)
Đáp án:
Giải thích các bước giải:
$a,3(1-4x)(x-1)+4(3x+2)(x+3)=38$
$(=)(3-12x)(x-1)+(12x+8)(x+3)=38$
$(=)3x-3-12x^2+12x+12x^2+36x+8x+24=38$
$(=)(3x+12x+36x+8x)-(12x^2-12x^2)=38+3-24$
$(=)59x=17$
$(=)x=\dfrac{1}{3}$
$b,5(2x+3)(x+2)-2(5x-4)(x-1)=75$
$(=)(10x+15)(x+2)-(10x-8)(x-1)=75$
$(=)10x^2+35x+30-10x^2+10x+8x-8=75$
$(=)53x=53$
$(=)x=1$
$c,2x^2+3(x-1)(x+1)=5x(x+1)$
$(=)2x^2+3x^2-3=5x^2+5x$
$(=)2x^2+3x^2-5x^2-5x=3$
$(=)x=\dfrac{-3}{5}$
$d,(8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0$
$(=)8x+16-5x^2-10x+4x^2+4x-8x-8+2x^2-8=0$
$(=)x^2-6x=0$
$(=)x(x-6)=0$
\(\left[ \begin{array}{l}x=0\\x=6\end{array} \right.\)
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