If ${\log _2}x + {\log _x}2 = \frac{{10}}{3} = {\log _2}y + {\log _y}2$ and $x \ne y,$ then $x + y = $

  • A

    $2$

  • B

    $65/8$

  • C

    $37/6$

  • D

    None of these

Similar Questions

If $\alpha ,\beta $are the roots of ${x^2} - ax + b = 0$ and if ${\alpha ^n} + {\beta ^n} = {V_n}$, then

The number of real solutions of the equation $\mathrm{x}|\mathrm{x}+5|+2|\mathrm{x}+7|-2=0$ is .....................

  • [JEE MAIN 2024]

If $a,b,c$ are distinct real numbers  and $a^3 + b^3 + c^3 = 3abc$ , then the equation $ax^2 + bx + c = 0$ has two roots, out of which one root is

The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is

Let $\alpha, \beta, \gamma$ be the three roots of the equation $x ^3+ bx + c =0$. If $\beta \gamma=1=-\alpha$, then $b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3$ is equal to $......$.

  • [JEE MAIN 2023]