已知a=(2+根号2)分之1,b=(2-根号3)分之1,求(2a+2b)分之(a的平方-b的平方)的值
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a=1/(2+√2),b=1/(2-√3)
原式=(a²-b²)/(2a+2b)
=(a-b)(a+b)/[2(a+b)]
=(a-b)/2
=[1/(2+√2)-1/(2-√3)]/2
={ (2-√2)/[(2-√2)(2+√2)]-(2+√3)/[(2+√3)(2-√3)] }/2
=[ (2-√2)/(2²-√2²)-(2+√3)/(2²-√3²) ]/2
=[ (2-√2)/(4-2)-(2+√3)/(4-3) ]/2
=[ (2-√2)/2-(2+√3) ]/2
=[ (2-√2)/2-2(2+√3)/2 ]/2
=[ (2-√2)-2(2+√3) ]/4
=(2-√2-4-2√3)/4
=(-2-√2-2√3)/4
原式=(a²-b²)/(2a+2b)
=(a-b)(a+b)/[2(a+b)]
=(a-b)/2
=[1/(2+√2)-1/(2-√3)]/2
={ (2-√2)/[(2-√2)(2+√2)]-(2+√3)/[(2+√3)(2-√3)] }/2
=[ (2-√2)/(2²-√2²)-(2+√3)/(2²-√3²) ]/2
=[ (2-√2)/(4-2)-(2+√3)/(4-3) ]/2
=[ (2-√2)/2-(2+√3) ]/2
=[ (2-√2)/2-2(2+√3)/2 ]/2
=[ (2-√2)-2(2+√3) ]/4
=(2-√2-4-2√3)/4
=(-2-√2-2√3)/4
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