Question

Solve $lo{g}_{10}[98+\sqrt{x^3-x^2-12x+14}]=2$

Answer 1

The equation can be written as
$98+\sqrt{x^3-x^2-12x+36}={10}^2=100$
or $\sqrt{x^3-x^2-12x+36}=2$
or $x^3-x^2-12x+36=4$
or $x^3-x^2-12x+32=0$
Now $(-64-16)+(48+32)=0$
$\therefore x=-4$ satisfies above .
or $(x+4)(x^2-5x+8)=0$
$\therefore x=-4$
or $x=\frac{5\pm \sqrt{25-32}}{2}=\frac{5\pm \sqrt{-7}}{2}$