ID#4227 BCS General Math Preli (43)

প্রদত্ত সমীকরণ: $4^x + 4^{1-x} = 4$

$\implies 4^x + \frac{4^1}{4^x} = 4$
$\implies 4^x + \frac{4}{4^x} = 4$

ধরি, $4^x = a$
$\implies a + \frac{4}{a} = 4$
$\implies \frac{a^2 + 4}{a} = 4$
$\implies a^2 + 4 = 4a$
$\implies a^2 - 4a + 4 = 0$
$\implies (a - 2)^2 = 0$
$\implies a - 2 = 0$
$\implies a = 2$

এখন $a$ এর মান বসিয়ে পাই:
$4^x = 2$
$\implies (2^2)^x = 2^1$
$\implies 2^{2x} = 2^1$
$\implies 2x = 1$
$\implies x = \frac{1}{2}$

সঠিক উত্তর: ক (1/2)