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4-2.Quadratic Equations and Inequations
hard
$2^x+3^y=5^{x y}$ को संतुष्ट करने वाले घनात्मक पूर्णांकों को क्रमित युग्मों $(x, y)$ की संख्या है.
A
$1$
B
$2$
C
$5$
D
अनंत
(KVPY-2020)
Solution
(a)
$\because 2^x+3^y=5^{x y}$
When $x=y=1$, then $2+3=5$ and $\left(\frac{2}{5}\right)^x \cdot \frac{1}{5^y}+\left(\frac{3}{5}\right)^y \cdot \frac{1}{5^x}=1$ here for any $x, y \in Z^{+}$LHS is not equal to 1 as both are less than $\frac{1}{2}$.
$\therefore$ Only one ordered pair $(1,1)$ is possible.
Standard 11
Mathematics
