Question

Set of solutions of the equation $3\left|\right(x-9{)}^2(x-1)|-6|x^2-10x+9|=0$ is

• A. $\{1,7,9\}$
• B. $\{1,7,9,11\}$
• C. $\{1,9,11\}$
• D. $\{1,9\}$

Answer 1

The correct option is B $\{1,7,9,11\}$

$3\left|\right(x-9{)}^2(x-1)|-6|x^2-10x+9|=0\Rightarrow 3|x-9||x-9||x-1|-6|x-9||x-1|=0\Rightarrow (3|x-9|-6)(|x-9||x-1|)=0$
$\Rightarrow 3|x-9|-6=0\text{or}|x-9|=0\text{or}|x-1|=0\Rightarrow x=11,7\text{or}x=9\text{or}x=1$
So, the solution set is $\{1,7,9,11\}$