Question

Find all the solutions of the equation $9x^2-18|x|+5=0$ belonging to the domain of definition of the function $y=\ln \left(\right(x+1)\times (x-2\left)\right).$

Answer 1

$(x+1)(x-2)\ge 0$

$x\in (-\infty ,-1)\cup (2,\infty )$

Let $\left|x\right|$ be $t$ , $t\ge 0$

$9t^2-18t+5=0$

$9t^2-3t-15t+5=0$

$(3t-5)(3t-1)=0$

$t=\frac{5}{3}or\frac{1}{3}$

$\left|x\right|=t$

$x=\pm \frac{5}{3},\pm \frac{1}{3}$

$x=-\frac{5}{3}$