x2 + 1/x2 = 3 হলে (x6 + 1)/x3 এর মান কত?
Solution
Correct Answer: Option C
এখন, (x6+1)/x3
=(x6/x3)+(1/x3)
=x3+ 1/x3
দেওয়া আছে,x2+ (1/x)2=3
or,(x+1/x)2-2.x.1/x=3
or,(x+1/x)2-2=3
or,(x+1/x)2=5
or,(x+1/x)=√5
∴ (x3+1/x3)=(x+1/x)3-3.x.1/x.(x+1/x)
=(√5)3-3√5
=5√5-3√5
=2√5
=(x6/x3)+(1/x3)
=x3+ 1/x3
দেওয়া আছে,x2+ (1/x)2=3
or,(x+1/x)2-2.x.1/x=3
or,(x+1/x)2-2=3
or,(x+1/x)2=5
or,(x+1/x)=√5
∴ (x3+1/x3)=(x+1/x)3-3.x.1/x.(x+1/x)
=(√5)3-3√5
=5√5-3√5
=2√5
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