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lg5+lg2*lg5+(lg2)^2=

(lg2)^2=lg2*lg2 (lg2)^2+lg2*lg5+lg5( =lg2*lg2+lg2*lg5+lg5(前两项提取公因式lg2) =lg2(lg2+lg5)+lg5 =lg2*1+lg5 =1

lg5+lg2*lg5+(lg2)^2 =lg5+lg2(lg5+lg2) =lg5+lg2 =1

lg5^2+2lg2-lg2^2 =2lg5+2lg2-2lg2 =2lg5; (lg5)^2+2lg2-(lg2)^2? =(lg5)^2-(lg2)^2+2lg2 =(lg5+lg2)(lg5-lg2)+lg2² =lg10*lg5/2+lg4 =1*lg5/2+lg4 =lg[(5/2)*4] =lg10 =1

lg5^2+2/3lg8+lg5*lg20+(lg2)^2 =2lg5+2/3lg2^3+lg5*lg5*2^2 +(lg2)^2 =2lg5+2/3 * 3 lg2+lg5(lg5+2lg2)+(lg2)^2 =2lg5+2lg2+(lg5)^2+2lg5lg2+(lg2)^2 =2(lg5+lg2)+(lg5)^2+2lg5lg2+(lg2)^2 =2lg10 + (lg5+lg2)^2 =2+(lg10)^2 =2+1=3

lg2*lg5 =lg(2*5) =lg10 =1 lg^25=lg5^2

利用lg5+lg2=1 原式=(lg5)²-(lg2)²+2lg2 =(lg5+lg2)(lg5-lg2)+2lg2 =lg5-lg2+2lg2 =lg5+lg2 =1

不是 lg2*lg5 =lg(10/5)*lg5 =(lg10-lg5)*lg5 =(1-lg5)*lg5 =lg5-(lg5)^2

lg5lg20+(lg2)^2 =lg5(lg2+lg10)+(lg2)^2 =lg5lg2+lg5+(lg2)^2 =lg2(lg5+lg2)+lg5 =lg2+lg5 =1

lg2+lg5=lg(2*5)=1

原式=2lg5+2lg2 +lg5(lg5+2lg2)+(lg2)^2 =2(lg5+lg2)+(lg2)^2+2lg2lg5+(lg5)^2 =2lg10+[lg2+lg5]^2 =2+1^2 =2+1 =3

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