1/√(5+2√6)+1/√(7+4√3)=?
问题描述：
1/√(5+2√6)+1/√(7+4√3)=?
答
5+2√6=3+2√6+2=(√3)^2+2*√3*√2+(√2)^2=(√3+√2)^2
7+4√3=4+4√3+3=2^2+2*2*√3+(√3)^2=(2+√3)^2
所以1/√(5+2√6)+1/√(7+4√3)
=1/√(√3+√2)^2+1/√(2+√3)^2
=1/(√3+√2)+1/(2+√3)
=(√3-√2)/(√3+√2)(√3-√2)+(2-√3)/(2+√3)(2-√3)
=(√3-√2)/(3-2)+(2-√3)/(4-3)
=√3-√2+2-√3
=2-√2
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