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a) \(\left(5x-2\right)\left(5x+2\right)-\left(5x+3\right)\left(5x-4\right)=0\)
\(\Leftrightarrow5x+8=8\)
\(\Leftrightarrow5x=8-8\)
\(\Leftrightarrow x=5.0\)
\(\Leftrightarrow x=0\)
b)
TÌM X biết:
a. (5x - 2)(5x + 2) - (5x + 3)(5x - 4) = 8
b. (4x - 3)( 4x + 2) + (4x + 5)(1 - 4x) =2.52
a ) \(\left(5x-2\right)\left(5x+2\right)-\left(5x+3\right)\left(5x-4\right)=8\)
\(\Leftrightarrow\left(5x\right)^2-4-\left(25x^2+15x-20x-12\right)=8\)
\(\Leftrightarrow25x^2-4-25x^2-15x+20x+12=8\)
\(\Leftrightarrow5x+8=8\)
\(\Leftrightarrow5x=0\)
\(\Leftrightarrow x=0\)
Vậy \(x=0\)
b ) \(\left(4x-3\right)\left(4x+2\right)+\left(4x+5\right)\left(1-4x\right)=2.5^2\)
\(\Leftrightarrow16x^2-12x+8x-6+4x+5-16x^2-20x=50\)
\(\Leftrightarrow-20x-1=50\)
\(\Leftrightarrow-20x=51\)
\(\Leftrightarrow x=-\dfrac{51}{20}\)
Vậy \(x=-\dfrac{51}{20}\)
Bài đã đăng rồi bạn lưu ý không đăng lại làm loãng box toán.
\(a,A=\left(x^2-x\right)\left(x^2-x-12\right)\\ A=\left(x^2-x\right)^2-12\left(x^2-x\right)\\ A=\left(x^2-x\right)^2-12\left(x^2-x\right)+36-36\\ A=\left(x^2-x+6\right)^2-36\ge-36\\ A_{min}=-36\Leftrightarrow x^2-x+6=0\Leftrightarrow\left(x-3\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\\ b,B=4x^4+4x^3+5x^2+4x+3\\ B=\left(4x^4+4x^3+x^2\right)+\left(x^2+4x+4\right)-1\\ B=x^2\left(2x+1\right)^2+\left(x+2\right)^2-1\ge-1\\ B_{min}=-1\Leftrightarrow\left\{{}\begin{matrix}x\left(2x+1\right)=0\\x+2=0\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
Vậy dấu \("="\) không xảy ra
a, \(4\left(18-5x\right)-12\left(3x-7\right)=15\left(2x-16\right)-6\left(x+14\right)\)
\(\Leftrightarrow72-20x-36x+84=30x-240-6x-84\)
\(\Leftrightarrow156-56x=24x-324\)
\(\Leftrightarrow-80x+480=0\Leftrightarrow x=-6\)
b, \(5\left(3x+5\right)-4\left(2x-3\right)=5x+3\left(2x-12\right)+1\)
\(\Leftrightarrow15x+25-8x+12=5x+6x-36+1\)
\(\Leftrightarrow7x+37=11x-35\)
\(\Leftrightarrow-4x+72=0\Leftrightarrow x=18\)
c, \(2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\)
\(\Leftrightarrow10x-16-12x+15=12x-16+11\)
\(\Leftrightarrow-2x-1=12x-5\)
\(\Leftrightarrow-14x+4=0\Leftrightarrow x=\frac{2}{7}\)
d, \(5x-3\left\{4x-2\left[4x-3\left(5x-2\right)\right]\right\}=182\)
\(\Leftrightarrow5x-3\left[4x-15x+6\right]=182\)
\(\Leftrightarrow5x-3\left(-11x+6\right)=182\)
\(\Leftrightarrow5x+33x-18-182=0\)
\(\Leftrightarrow38x-200=0\Leftrightarrow x=\frac{100}{19}\)