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4-2.Quadratic Equations and Inequations
medium
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
Solution
(d) We have ${\log _2}x + \frac{1}{{{{\log }_2}x}} = 3 + \frac{1}{3} = {\log _2}y + \frac{1}{{{{\log }_2}y}}$
$\therefore$ ${\log _2}x = 3,{\log _2}y = \frac{1}{3}$ $(x \ne y)$
==> $x = {2^3}$and$y = {2^{1/3}}$
$\Rightarrow x + y = 8 + {2^{1/3}}$.
Standard 11
Mathematics
