Question

The product of real roots of the equation $|x{|}^{\frac{6}{5}}-26|x{|}^{\frac{3}{5}}-27=0$ is

• A. $-3^{10}$
• B. $-3^{12}$
• C. $-3^{\frac{12}{5}}$
• D. $-3^{\frac{21}{5}}$

Answer 1

The correct option is A $-3^{10}$

$|x{|}^{\frac{6}{5}}-26|x{|}^{\frac{3}{5}}-27=0$

Let $|x{|}^{\frac{3}{5}}=t$

$\Rightarrow t^2-26t-27=0$

$\Rightarrow t^2-27t+t-27=0$

$\Rightarrow t(t-27)+1(t-27)=0$

$\Rightarrow (t+1)(t-27)=0$

$t=27$ or $-1$

$|x{|}^{\frac{3}{5}}=27$

$x=+3^{5}or-3^5$

Product $=3^5\cdot (-3{)}^5=-3^{10}$