x2-√5x +1=0, find value of x2-1/x2
Solution
Correct Answer: Option B
দেওয়া আছে, x2 - √5x + 1 = 0
বা, x2 + 1 = √5x
বা, x + 1/x = √5
এখন, (x - 1/x)2 = (x + 1/x)2 - 4x(1/x)
বা, (x - 1/x)2 = (√5)2 - 4
বা, (x - 1/x)2 = 5 - 4
∴ x - 1/x = 1
প্রদত্ত রাশি, x2 - 1/x2 = (x + 1/x)(x - 1/x) = √5 × 1 = √5
বা, x2 + 1 = √5x
বা, x + 1/x = √5
এখন, (x - 1/x)2 = (x + 1/x)2 - 4x(1/x)
বা, (x - 1/x)2 = (√5)2 - 4
বা, (x - 1/x)2 = 5 - 4
∴ x - 1/x = 1
প্রদত্ত রাশি, x2 - 1/x2 = (x + 1/x)(x - 1/x) = √5 × 1 = √5
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