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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Number of distinct integer values of $a$ satisfying
$2^{2a} - 3(2^{a+2}) + 25 = 0$ is:
Solution
Rewrite: $2^{2a} - 12\cdot 2^a + 25 = 0$Let $t = 2^a$ (positive).
Equation becomes:
$t^2 - 12t + 25 = 0$
$t = \dfrac{12 \pm \sqrt{44}}{2} = 6 \pm \sqrt{11}$
We need $t = 2^a$, a power of 2.
Check if $6 + \sqrt{11}$ or $6 - \sqrt{11}$ is a power of 2.
Values:
$6 + \sqrt{11} \approx 9.316$ → not power of 2
$6 - \sqrt{11} \approx 2.684$ → not power of 2
No integer $a$ exists.
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