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Trả lời:
a, \(x^2-9-2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+3\right)-2\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+3-2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\x+1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-1\end{cases}}}\)
Vậy x = 3; x = - 1 là nghiệm của pt.
b, \(x\left(x-5\right)-4x+20=0\)
\(\Leftrightarrow x\left(x-5\right)-4\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=4\end{cases}}}\)
Vậy x = 5; x = 4 là nghiệm của pt.
c, \(2x^2+3x-5=0\)
\(\Leftrightarrow2x^2+5x-2x-5=0\)
\(\Leftrightarrow x\left(2x+5\right)-\left(2x+5\right)=0\)
\(\Leftrightarrow\left(2x+5\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x+5=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{5}{2}\\x=1\end{cases}}}\)
Vậy x = - 5/2; x = 1 là nghiệm của pt.
\(\Leftrightarrow5\left(x-4\right)-\left(x-4\right)^2=0\\ \Leftrightarrow\left(x-4\right)\left(5-x+4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(9-x\right)=0\Leftrightarrow\left[{}\begin{matrix}x=4\\x=9\end{matrix}\right.\)
\(-x^4+4x^2-5x^2+20=0\\\Rightarrow -(x^4-4x^2)-(5x^2-20)=0\\\Rightarrow-x^2(x^2-4)-5(x^2-4)=0\\\Rightarrow(x^2-4)(-x^2-5)=0\\\Rightarrow-(x-2)(x+2)(x^2+5)=0\\\Rightarrow(2-x)(x+2)=0(vì.x^2+5>0\forall x)\)
\(\Rightarrow\left[{}\begin{matrix}2-x=0\\x+2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
a) Ta có: \(7x\left(x-20\right)-x+20=0\)
\(\Leftrightarrow\left(x-20\right)\left(7x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=20\\x=\dfrac{1}{7}\end{matrix}\right.\)
b) Ta có: \(x^3-15x=0\)
\(\Leftrightarrow x\left(x-\sqrt{15}\right)\left(x+\sqrt{15}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt{15}\\x=-\sqrt{15}\end{matrix}\right.\)
a) x2 + 10x - 2x - 20 = 0
=> x(x + 10) - 2(x + 10) = 0
=> (x - 2)(x + 10) = 0
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x+10=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-10\end{cases}}\)
b) \(x^2-5x-24=0\)
\(\Rightarrow x^2-5x+\frac{25}{4}-\frac{121}{4}=0\)
\(\Rightarrow\left(x-\frac{5}{2}\right)^2=\frac{121}{4}\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-\frac{5}{2}\right)^2=\left(-\frac{11}{2}\right)^2\\\left(x-\frac{5}{2}\right)^2=\left(\frac{11}{2}\right)^2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{5}{2}=\left(-\frac{11}{2}\right)\\x-\frac{5}{2}=\frac{11}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{6}{2}=3\\x=\frac{16}{2}=8\end{cases}}\)
c) x2 - 8x + 3x - 24 = 0
=> x(x - 8) + 3(x - 8) = 0
=> (x + 3)(x - 8) = 0
\(\Leftrightarrow\orbr{\begin{cases}x+3=0\\x-8=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-3\\x=8\end{cases}}\)
Ko viết lại đề
Câu 1: chia ra làm 3 trường hợp
Câu 2:
\(\left(x+2-x+2\right)\left(x+2\right)=0\)
\(4\left(x+2\right)=0\)
\(\Rightarrow x+2=0\)
\(x=-2\)
Ta có : 5x + 20 - x2 - 4x = 0
=> 5(x + 4) - (x2 + 4x) = 0
=> 5(x + 4) - x(x + 4) = 0
=> (x + 4) ( 5 - x) = 0
\(\Rightarrow\orbr{\begin{cases}x+4=0\\x-5=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=5\end{cases}}\)
b) tương tự nhá
\(a.5x+20-x^2-4x=0\)
\(\Leftrightarrow5\left(x+4\right)-x\left(x+4\right)=0\)
\(\Leftrightarrow\left(5-x\right)\left(x+4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}5-x=0\\x+4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-4\end{cases}}\)
\(b.x^2+3x-\left(2x+6\right)=0\)
\(\Leftrightarrow x^2+3x-2x-6=0\)
\(\Leftrightarrow x\left(x+3\right)-2\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-3\end{cases}}\)
Answer:
\(x^2-x-20=0\)
\(\Rightarrow x^2+4x-5x-20=0\)
\(\Rightarrow x\left(x+4\right)-5\left(x+4\right)=0\)
\(\Rightarrow\left(x+4\right)\left(x-5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+4=0\\x-5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-4\\x=5\end{cases}}}\)