\(x^4-10x^2+9=0\)
\(\Leftrightarrow x^4-x^2-9x^2+9x=0\)
\(\Leftrightarrow x^2\left(x^2-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow x^2\left(x+1\right)\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^3+x^2\right)\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^3+x^2-9\right)\left(x-1\right)=0\)
<=> x - 1 = 0 (vì x3 + x2 - 9)
<=> x = 1
a) Ta có: \(x^4-10x^2+9=0\)
\(\Rightarrow x^4-x^2-9x^2+9=0\)
\(\Rightarrow x^2\left(x^2-1\right)-9\left(x^2-1\right)=0\)
\(\Rightarrow\left(x^2-9\right)\left(x^2-1\right)=0\)
\(\Rightarrow x^2-9=0\)hoặc \(x^2-1=0\)
\(\Rightarrow x^2=9\)hoặc \(x^2=1\)
\(\Rightarrow\)x= -3 hoặc x = 3 hoặc x = -1 hoặc x = 1.
b) \(x^2-3x-18=0\)
\(\Rightarrow x^2+6x-3x-18=0\)
\(\Rightarrow x\left(x+6\right)-3\left(x+6\right)=0\)
\(\Rightarrow\left(x-3\right)\left(x+6\right)=0\)
\(\Rightarrow x-3=0\)hoặc \(x+6=0\)
\(\Rightarrow x=3\)hoặc \(x=-6\).
Chúc bn hc tốt! ^_^
#Ttql nhia mn!
