`-15x^2+170x-55=0`
`<=>15x^2-170x+55=0`
`<=>(15x^2-165x)-(5x-55)=0`
`<=>15x(x-11)-5(x-11)=0`
`<=>(15x-5)(x-110)=0`
`<=>` \(\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=11\end{matrix}\right.\)
\(-15x^2+170x-55=0\)
\(\Delta=170^2-4.\left(-15\right).\left(-55\right)\)
\(=28900-3300\)
\(=25600>0\Rightarrow\sqrt{\Delta}=160\)
\(\Rightarrow\)Phương trình có 2 nghiệm phân biệt:
\(x_1=\dfrac{-170-160}{2.\left(-15\right)}=11\) \(x_2=\dfrac{-170+160}{2.\left(-15\right)}=\dfrac{1}{3}\)
Vậy phương trình có 2 nghiệm là x1=11;x2=\(\dfrac{1}{3}\)
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TK
\(-15x^2+170x-55=0\)
\(15x^2-170x+55\)
\(15x^2-165x-5x-55=0\)
\(\left(15x^2-165x\right)-\left(5x-55\right)=0\)
\(15x\left(x-11\right)-5\left(x-11\right)\)
\(\left(x-11\right)\left(15x-5\right)=0\)
\(\left[{}\begin{matrix}x=11\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy \(x\in\left\{\dfrac{1}{3};11\right\}\)