x-2=√3 হলে x⁴+(1/x⁴) এর মান কত ?
Solution
Correct Answer: Option B
x-2=√3
বা,x=2+√3
∴1/x=1(2+√3)
(2-√3)/((2+√3)(2-√3)
=(2-√3)/2²-(√3)²
=(2-√3)/(4-3)
=2-√3
অতএব,
x+1/x=2+√3+2-√3
=4
অতএব,
x⁴+1/x⁴ =(x²)²+(1/x²)²
=(x²+1/x²)²-2.x².1/x²
={(x+1/x)²-2.x.1/x}²-2
={(4)²-2}²-2
=(16-2)²-2
=196-2
=194
বা,x=2+√3
∴1/x=1(2+√3)
(2-√3)/((2+√3)(2-√3)
=(2-√3)/2²-(√3)²
=(2-√3)/(4-3)
=2-√3
অতএব,
x+1/x=2+√3+2-√3
=4
অতএব,
x⁴+1/x⁴ =(x²)²+(1/x²)²
=(x²+1/x²)²-2.x².1/x²
={(x+1/x)²-2.x.1/x}²-2
={(4)²-2}²-2
=(16-2)²-2
=196-2
=194
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