Question
Download Solution PDFযদি \(x^{2} - 5x + 1 = 0,\) হয়, তাহলে \(\frac{x^{6}+x^{4}+x^{2}+1}{5x^{3}}=?\) এর মান কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
\(x^{2} - 5x + 1 = 0\)
অনুসৃত ধারণা:
যদি a + 1/a = b হয়, তাহলে
a3 + 1/a3 = b3 - 3b
গণনা:
x2 - 5x + 1 = 0
⇒ x2 + 1 = 5x
⇒ x + 1/x = 5
এখন,
\(\frac{x^{6}+x^{4}+x^{2}+1}{5x^{3}}\)
⇒ \(\frac{x^{3}+x+\frac{1}{x}+\frac{1}{x^3}}{5}\) [\(\frac{1}{x^3}\) দ্বারা ভাগ করে পাই]
⇒ \(\frac{5^3 -3\times5+5}{5}\)
⇒ \(\frac{125 - 15 +5}{5}\)
⇒ \(\frac{115}{5}\)
⇒ 23
∴ নির্ণেয় উত্তর হল 23
Last updated on Jul 19, 2025
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