đag chơi thì
11x 2 + 15x 6 +16 x2
tính nhanh
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\(a,Sửa:x^2-16-15x\left(x-4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(x+4\right)-15x\left(x-4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(-14x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{2}{7}\end{matrix}\right.\\ b,\Leftrightarrow x^2-x-7x+7=0\\ \Leftrightarrow\left(x-1\right)\left(x-7\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=7\end{matrix}\right.\\ c,\Leftrightarrow6x^2-9x-2x+3=0\\ \Leftrightarrow\left(2x-3\right)\left(3x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
\(11x^2-15x+4=0\)
\(\Leftrightarrow11x^2-11x-4x+4=0\)
\(\Leftrightarrow11x\left(x-1\right)-4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(11x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\11x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{4}{11}\end{matrix}\right.\)
\(S=\left\{1,\dfrac{4}{11}\right\}\)
Đặt C(x)=0
\(\Leftrightarrow11x^2-15x+4=0\)
\(\Leftrightarrow11x^2-11x-4x+4=0\)
\(\Leftrightarrow11x\left(x-1\right)-4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(11x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\11x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\11x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{4}{11}\end{matrix}\right.\)
Vậy: Nghiệm của đa thức \(C\left(x\right)=11x^2-15x+4\) là 1 và \(\dfrac{4}{11}\)
a) \(x^3+x^2+5x^2+5x+6x+6=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
b) \(x^3-3x^2+9x^2-27x+14x-42\)
\(=x^2\left(x+3\right)+9x\left(x+3\right)+14\left(x+3\right)\)
\(=\left(x^2+9x+14\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(x+2\right)\left(x+7\right)\)
c) \(\left(x^2+x+4\right)^2+3x\left(x^2+x+4\right)+5x\left(x^2+x+4\right)+15x^2\)
\(=\left(x^2+x+4\right)\left(x^2+x+4+3x\right)+5x\left(x^2+x+4+3x\right)\)
\(=\left(x^2+6x+4\right)\left(x^2+4x+4\right)\)
\(=\left(x^2+6x+4\right)\left(x+2\right)^2\)
d) \(\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x\right)^2+40\left(x^2+10x\right)+16.24+16\)
\(=\left(x^2+10x\right)^2+40\left(x^2+10x\right)+400\)
\(=\left(x^2+10x+20\right)^2\)
help
\(=11\times2+15\times2\times3+16\times2\\ =2\times\left(11+15+16\right)\times3\\ =2\times42\times3\\ =252\)