Question

If $x_1, x_2 \& x_3$ are the three real solutions of the equation $x^{\log _{10}^2 x+\log _{10} x^3+3}=\frac{2}{\frac{1}{\sqrt{x+1}-1}-\frac{1}{\sqrt{x+1}+1}}$ where $x_1>x_2>x_3$, then

• A. $x_1+x_3=2 x_2$
• B. $x _1 \cdot x _3= x _2{ }^2$
• C. $x_2=\frac{2 x_1 x_2}{x_1+x_2}$
• D. $x_1^{-1}+x_2^{-1}=x_3^{-1}$

Answer 1

Answer: (B)

RHS when simplified is equal $x$
$x_1=1 ; x_2=\frac{1}{10} ; x_3=\frac{1}{100}$
$\log _{10} x^2 \ln =1 \sin =0 ; x=1$