x=√4+√3 হলে, x3+(1/x3) এর মান কত?
Solution
Correct Answer: Option B
দেওয়া আছে
x = √4 + √3
বা, 1/x = 1/(√4 + √3)
বা, 1/x = (√4 - √3)/(√4 - √3)(√4 + √3)
বা, 1/x = (√4 - √3)/{(√4)2 - (√3)2}
বা, 1/x = (√4 - √3)/(4 - 3)
বা, 1/x = (√4 - √3)/1
বা, 1/x = (√4 - √3)
এখন
x + 1/x = √4 + √3 + √4 - √3
= 2√4
= 2 × 2
= 4
আমরা জানি
x3 + 1/x3 = (x + 1/x)3 - 3.x.1/x(x + 1/x)
= 43 - 3 × 4
= 64 - 12
= 52
x = √4 + √3
বা, 1/x = 1/(√4 + √3)
বা, 1/x = (√4 - √3)/(√4 - √3)(√4 + √3)
বা, 1/x = (√4 - √3)/{(√4)2 - (√3)2}
বা, 1/x = (√4 - √3)/(4 - 3)
বা, 1/x = (√4 - √3)/1
বা, 1/x = (√4 - √3)
এখন
x + 1/x = √4 + √3 + √4 - √3
= 2√4
= 2 × 2
= 4
আমরা জানি
x3 + 1/x3 = (x + 1/x)3 - 3.x.1/x(x + 1/x)
= 43 - 3 × 4
= 64 - 12
= 52
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