证明√(a^2+1/(b^2)+a^2/(ab+1)^2)=|a+1/b-a/(ab+1)|
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证明√(a^2+1/(b^2)+a^2/(ab+1)^2)=|a+1/b-a/(ab+1)|
√(a^2+1/(b^2)+a^2/(ab+1)^2)
=√(a^2+1)(ab+1)^2/(b^2)(ab+1)^2+a^2*b^2/(ab+1)^2*b^2)
=√(a^2+1)(ab+1)^2+(ab)^2/(b^2)(ab+1)^2)
=√[(a^2+1)(a^2*b^2+2ab+1)+(ab)^2]/(b^2)(ab+1)^2)
=√[a^4*b^2+a^2*b^2+a^2+1+2a^3*b+2ab+(ab)^2]/(b^2)(ab+1)^2)
=√[a^4*b^2+a^2+1+2a^3*b+2ab+2(ab)^2]/(b^2)(ab+1)^2)
=√[(ab+1)^2-ab]^2/(b^2)(ab+1)^2)
=|[(ab+1)^2-ab]/b(ab+1)|
=|a+1/b-a/(ab+1)|
=√(a^2+1)(ab+1)^2/(b^2)(ab+1)^2+a^2*b^2/(ab+1)^2*b^2)
=√(a^2+1)(ab+1)^2+(ab)^2/(b^2)(ab+1)^2)
=√[(a^2+1)(a^2*b^2+2ab+1)+(ab)^2]/(b^2)(ab+1)^2)
=√[a^4*b^2+a^2*b^2+a^2+1+2a^3*b+2ab+(ab)^2]/(b^2)(ab+1)^2)
=√[a^4*b^2+a^2+1+2a^3*b+2ab+2(ab)^2]/(b^2)(ab+1)^2)
=√[(ab+1)^2-ab]^2/(b^2)(ab+1)^2)
=|[(ab+1)^2-ab]/b(ab+1)|
=|a+1/b-a/(ab+1)|
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