x2 + √2x + 1 = 0 হলে, x12 + 1/x6 এর মান কত?
Solution
Correct Answer: Option A
দেওয়া আছে, x2 + √2x + 1 = 0
⇒ x - √2 + 1/x = 0
[x দ্বারা উভয় পক্ষকে ভাগ করে]
⇒ x + 1/x = √2
∴ x12 + 1/x6 = x12/x6 + 1/x6
= x6 + 1/x6 = (x3)2 + (1/x3)2
= (x3 + 1/x3)2 - 2.x3.1/x3
= {(x + 1/x)3 - 3x.1/x (x + 1/x)}2 - 2
= {(√2)3 - 3.√2}2 - 2
= (2√2 - 3√2)2 -2
= (-√2)2 - 2
= 2 - 2
= 0