作业帮化简log2(1+2^0.5+3^0.5)+ log2(1+2^0.5-3^0.5)
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/16 07:01:08
化简log2(1+2^0.5+3^0.5)+ log2(1+2^0.5-3^0.5)
化简log2(1+2^0.5+3^0.5)+ log2(1+2^0.5-3^0.5)
化简log2(1+2^0.5+3^0.5)+ log2(1+2^0.5-3^0.5)
原式=log2[(1+√2+√3)(1+√2-√3)]
(1+√2+√3)(1+√2-√3)
=(1+√2)^2-(√3)^2
=1+2√2+2-3
=2√2
=2*2^(1/2)
=2^(3/2)
所以原式=log2[2^(3/2)]=3/2
=log2(1+2^0.5+3^0.5)(1+2^0.5-3^0.5)
=log2[(1+2^0.5)^2-(3^0.5)^2]
=log2[1+2+2根号2-3]
=log2(2根号2)
=3/2
化简log2(1+2^0.5+3^0.5)+ log2(1+2^0.5-3^0.5)
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