Question

3x la puterea a2a - 8x+16 supra 6(x+3)-4(x+6)<0

Answer 1

$\frac{3x^2-8x+16}{6\left(x+3\right)-4\left(x+6\right)}\ \textless \ 0 \\ \\ Luam : 6\left(x+3\right)-4\left(x+6\right)=6x+18-4\left(x+6\right) \\ \\ =6x+18-4x-24=2x-6 \\ \\ Deci:\frac{3x^2-8x+16}{6\left(x+3\right)-4\left(x+6\right)}=\frac{3x^2-8x+16}{2x-6} \\ \\ \frac{3x^2-8x+16}{2x-6}\ \textless \ 0 \\ \\ \frac{3x^2-8x+16}{2\left(x-3\right)}\ \textless \ 0 \\ \\ 3x^2-8x+16\ \textgreater \ 0 \\ \\ \left(\sqrt{3}x-\frac{4}{\sqrt{3}}\right)^2+\frac{32}{3}\ \textgreater \ 0 \\ \\ \left(\sqrt{3}x-\frac{4}{\sqrt{3}}\right)^2\ \textgreater \ -\frac{32}{3} \\ \\ x\ \textless \ 3$