Toán Lớp 9: giải phương trình
( $x^{2}$ + 2$x^{}$ ) ²-14.( $x^{2}$ + 2$x^{}$ )-15=0
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Toán Lớp 9: giải phương trình
( $x^{2}$ + 2$x^{}$ ) ²-14.( $x^{2}$ + 2$x^{}$ )-15=0
Comments ( 2 )
$\left(x^2+2x\right)^2-14\left(x^2+2x\right)-15=0$
$⇔x^4+4x^3-10x^2-28x-15=0$
$⇔\left(x+1\right)^2\left(x-3\right)\left(x+5\right)=0$
\(⇔\left[ \begin{array}{l}x+1=0\\x-3=0\\x+5=0\end{array} \right.\) \(⇔\left[ \begin{array}{l}x=-1\\x=3\\x=-5\end{array} \right.\)
$\text{Vậy pt có nghiệm {-1 ; 3 ; -5}}$
$ ( x^2 – 2x )^2 – 14.(x^2+2x)-15=0 $
$ ⇒ (x^2+2x)^2 + (x^2+2x)-15(x^2+2x)-15=0 $
$ ⇒ (x^2+2x)(x^2+2x+1)-15(x^2+2x+1)=0 $
$ ⇒ (x+1)^2 . (x^2+2x-15)=0 $
$ ⇒ (x+1)^2 . (x+5).(x-3)=0 $
$ ⇒ $ \(\left[ \begin{array}{l}(x+1)^2=0⇒x+1=0\\x+5=0\\x-3=0\end{array} \right.\)
$ ⇒ $ \(\left[ \begin{array}{l}x=-1\\x=-5\\x=3\end{array} \right.\)
$ ⇒ x = -1;-5;3 $