যদি \(\sqrt x + \frac{1}{{\sqrt x }} = a\) হয়, তবে \({x^2} + \frac{1}{{{x^2}}}\) -এর মান কত?
Solution
Correct Answer: Option D
√x + 1/√x = a
বা, (√x + 1/√x)² = a²
বা, x + 2 + 1/x = a²
বা, x + 1/x = a² - 2
x² + 1/x²
= (x + 1/x)²
বা,(x + 1/x)² = (a² - 2)²
বা, x² + 2 + 1/x² = a⁴ - 4a² + 4
বা, x² + 1/x² = a⁴ - 4a² + 4 - 2
সুতরাং, x² + 1/x² = a⁴ - 4a² + 2
বা, (√x + 1/√x)² = a²
বা, x + 2 + 1/x = a²
বা, x + 1/x = a² - 2
x² + 1/x²
= (x + 1/x)²
বা,(x + 1/x)² = (a² - 2)²
বা, x² + 2 + 1/x² = a⁴ - 4a² + 4
বা, x² + 1/x² = a⁴ - 4a² + 4 - 2
সুতরাং, x² + 1/x² = a⁴ - 4a² + 2
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