已知a=1/(2+根号3),化简求值1/a+根号下(1/a²+a²-2)
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已知a=1/(2+根号3),化简求值1/a+根号下(1/a²+a²-2)
已知a=1/(2+根号3),化简求值1/a+根号下(1/a²+a²-2)
已知a=1/(2+根号3),化简求值1/a+根号下(1/a²+a²-2)
解
a=1/(2+√3)=(2-√3)/(2+√3)(2-√3)=2-√3
又1/a=2+√3
∴1/a+√(1/a²+a²-2)
=1/a+√(1/a-a)²
=1/a+1/a-a
=2/a-a
=2×(2+√3)-(2-√3)
=4+2√3-2+√3
=2+3√3
2+3✔3