x=√4+√3 হলে x3+1/x3 এর মান কত?
Solution
Correct Answer: Option B
দেওয়া আছে x=√4+√3
or,1/x = 1/(√4+√3)
= (√4-√3)/(√4+√3)(√4-√3)
= (√4-√3)/ {(√4)2 -(√3)2}
= (√4-√3)/(4-3)
= √4-√3
তাহলে (x+1/x)= (√4+√3) + (√4-√3)
= 2√4
এখন,x3+1/x3
= (x)3 + (1/x)3
= (x+1/x) - 3.x.1/x (x+1/x)
= (2√4)3 - 3(2√4)
= 8.4√4 - 6√4
= 32√4 - 6√4
= 26√4
= 26×2
= 52
or,1/x = 1/(√4+√3)
= (√4-√3)/(√4+√3)(√4-√3)
= (√4-√3)/ {(√4)2 -(√3)2}
= (√4-√3)/(4-3)
= √4-√3
তাহলে (x+1/x)= (√4+√3) + (√4-√3)
= 2√4
এখন,x3+1/x3
= (x)3 + (1/x)3
= (x+1/x) - 3.x.1/x (x+1/x)
= (2√4)3 - 3(2√4)
= 8.4√4 - 6√4
= 32√4 - 6√4
= 26√4
= 26×2
= 52
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