Question

Tìm x nguyên dương để \(4x^3+14x^2+9x-6=0\)

Answer 1

4x³+8x²+6x²+12x-3x-6=0

=> 4x²(x+2)+6x(x+2)-3(x+2)=0

=> (4x²+6x-3)(x+2)=0

=> \(\left[{}\begin{matrix}4x^2+6x-3=0\\x+2=0\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}\left(2x+\dfrac{3}{2}\right)^2=\dfrac{21}{4}\\x=-2\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}\left[{}\begin{matrix}x=\dfrac{\sqrt{21}-3}{4}\\x=\dfrac{-\sqrt{21}-3}{4}\end{matrix}\right.\\x=-2\end{matrix}\right.\)