solve: x^9 −2x^5 −3x=0


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Question Number 171846 by Mikenice last updated on 21/Jun/22

$s o l v e :$ $x^{9} - 2 x^{5} - 3 x = 0$
Commented by kaivan.ahmadi last updated on 21/Jun/22
$x(x^8 −2x^4 −3)=0⇒{_(x^8 −2x^4 −3=0) ^(x=0) y=x^4 ⇒y^2 −2y−3=0⇒ (y−3)(y+1)=0⇒{_(y+1=0⇒y=−1) ^(y−3=0⇒y=3) if y=3⇒x^4 =3⇒x=(3)^(1/4) if y=−1⇒x^4 =−1 there is no real answer$
$x (x^{8} - 2 x^{4} - 3) = 0 \Rightarrow {_{x^{8} - 2 x^{4} - 3 = 0}^{x = 0}$ $y = x^{4} \Rightarrow y^{2} - 2 y - 3 = 0 \Rightarrow$ $(y - 3) (y + 1) = 0 \Rightarrow {_{y + 1 = 0 \Rightarrow y = - 1}^{y - 3 = 0 \Rightarrow y = 3}$ $i f y = 3 \Rightarrow x^{4} = 3 \Rightarrow x = \sqrt[4]{3}$ $i f y = - 1 \Rightarrow x^{4} = - 1 t h e r e i s n o r e a l a n s w e r$
Commented by Mikenice last updated on 23/Jun/22

$t h a n k s s i r$
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