x=√3+√2 হলে x²+1/x² এর মান কত?
Solution
Correct Answer: Option A
দেওয়া আছে ,
x=√3+√2
অতএব, 1/x =1 /(√3+√2 )
=(√3-√2 )/ (√3+√2 )(√3-√2 )
=(√3-√2)/3-2
=(√3-√2)/1
=√3-√2
অতএব, x+1/x=√3+√2 +√3-√2
=2√3
এখন ,x²+1/x² =( x+1/x)²-2.x.1/x
=(2√3)²-2
=12-2
=10
x=√3+√2
অতএব, 1/x =1 /(√3+√2 )
=(√3-√2 )/ (√3+√2 )(√3-√2 )
=(√3-√2)/3-2
=(√3-√2)/1
=√3-√2
অতএব, x+1/x=√3+√2 +√3-√2
=2√3
এখন ,x²+1/x² =( x+1/x)²-2.x.1/x
=(2√3)²-2
=12-2
=10
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