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A=123^2 + 54.123 + 77^2
= 123^2 + 2.123.77 + 77^2 - (154-54).123
= (123+77)^2 - 100.123
= 200^2 -12300
= 40000-12300
= 27700.
a) \(A=123\left(123+154\right)+77^2\)
\(A=123^2+\left(123.154\right)+77^2=\left(123+77\right)^2=200^2=400\)
b) \(B=3^{24}-\left(2^{47}+1\right)\left(9^6-1\right)\)
\(B=3^{24}-\left(3^{12}-1\right)\left(3^{12}+1\right)\)
\(B=3^{24}-3^{24}+1=1\)
c) \(C=85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2\)
\(C=\left(85^2-15^2\right)+\left(75^2-25^2\right)+\left(65^2-35^2\right)+\left(55^2-45^2\right)\)
\(C=\left(85+15\right)\left(85-15\right)+\left(75+25\right)\left(75-25\right)+\left(65+35\right)\left(65-35\right)\left(55+45\right)\left(55-45\right)\)
\(C=100\left(60+50+40+30+20+10\right)\)
\(C=100.210=21000\)
B=\(3^{24}-\left(27^4+1\right)\left(9^6+1\right)=-1062883\)A=123(123+154)+772=123.277+772=34843
C=\(85^2+75^2+65^2+55^2-45^2-35^2-25^2-15^2=16000\)
123² - 123.46 + 23²
= 123² - 2.123.23 + 23²
= (123 - 23)²
= 100²
= 10000
Lời giải:
a)
\(A=75^2+50.75+25^2=75^2+2.25.75+25^2\)
\(=(75+25)^2=100^2=10000\)
b) \(123^2+23^2-46.123=123^2-2.23.123+23^2\)
\(=(123-23)^2=100^2=10000\)
c) \((3^4-1)(3^4+1)-9^4\)
\(=[(3^4)^2-1^2]-9^4=(9^4-1)-9^4=-1\)
(1/2+2/5+7/3+5/9+123/159).((252-2.25.15+152)-100)
=(1/2+2/5+7/3+5/9+123/159).((25-15)2-100)
=(1/2+2/5+7/3+5/9+123/159).(102-100)
=(1/2+2/5+7/3+5/9+123/159).(100-100)
=(1/2+2/5+7/3+5/9+123/159).0=0