计算(2+√3)/[√2+√(2+√3)]+(2-√3)/[√2-√(2-√3)]=？
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(2+√3)/[√2+√(2+√3)]+(2-√3)/[√2-√(2-√3)]
=(2+√3)/[√2+√(√3+1)²/2]+(2-√3)/[√2-√(√3-1)²/2]
=(2+√3)/[√2+(√3+1)/√2]+(2-√3)/[√2-(√3-1)/√2]
=(2+√3)/[√2+1/2√6+1/2√2]+(2-√3)/[√2-1/2√3+1/2√2]
=(2+√3)/[3/2√2+1/2√6]+(2-√3)/[3/2√2-1/2√6]
=(4+2√3)/[3√2+√6]+(4-2√3)/[3√2-√6]
=(12√2+4√6+6√6+6√2]/(18-6)+(12√2-4√6-6√6+6√2]/(18-6)
=(18√2+10√6]/(18-6)+(18√2-10√6]/(18-6)
=36√2/12
=3√2
=(2+√3)/[√2+√(√3+1)²/2]+(2-√3)/[√2-√(√3-1)²/2]
=(2+√3)/[√2+(√3+1)/√2]+(2-√3)/[√2-(√3-1)/√2]
=(2+√3)/[√2+1/2√6+1/2√2]+(2-√3)/[√2-1/2√3+1/2√2]
=(2+√3)/[3/2√2+1/2√6]+(2-√3)/[3/2√2-1/2√6]
=(4+2√3)/[3√2+√6]+(4-2√3)/[3√2-√6]
=(12√2+4√6+6√6+6√2]/(18-6)+(12√2-4√6-6√6+6√2]/(18-6)
=(18√2+10√6]/(18-6)+(18√2-10√6]/(18-6)
=36√2/12
=3√2
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