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\(a,\frac{63^2-47^2}{215^2-105^2}=\frac{\left(63-47\right)\left(63+47\right)}{\left(215-105\right)\left(215+105\right)}=\frac{16.110}{110.320}=\frac{1}{20}\)
\(b,\frac{437^2-363^2}{537^2-463^2}=\frac{\left(437-363\right)\left(437+363\right)}{\left(537-463\right)\left(537+463\right)}=\frac{74.800}{74.1000}=0,8\)
\(c,2^{32}-\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=2^{32}-\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=2^{32}-\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=2^{32}-\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=2^{32}-\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-2^{32}+1=1\)
\(d,100^2+103^2+105^2+94^2-101^2-98^2-96^2-107^2\)
\(=\left(100^2-98^2\right)+\left(103^2-101^2\right)-\left(107^2-105^2\right)-\left(96^2-94^2\right)\)
\(=\left(100-98\right)\left(100+98\right)+\left(103-101\right)\left(103+101\right)-\left(107-105\right)\left(107+105\right)-\left(96-94\right)\left(96+94\right)\)
\(=2.198+2.204-2.212-2.190\)
\(=2\left(198+204-212-190\right)=2.0=0\)
a) 1272 + 146.127 + 732
= 1272 + 2.73.127 + 732
= (127 + 73)2 = 2002 = 40000
b) 98 . 28 - (184 - 1)(184 + 1)
= (9.2)8 - 188 + 1
= 188 - 188 + 1 = 1
c) \(\frac{780^2-220^2}{125^2+150.125+75^2}=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2.75.125+75^2}=\frac{560.1000}{\left(125+75\right)^2}=\frac{560000}{200^2}\)
\(=\frac{560000}{40000}=14\)
a) 1272 + 146.127 + 732
= 1272 + 2.73.127 + 732
= ( 127 + 73 )2
= 2002 = 40 000
b) 98.28 - ( 184 - 1 )( 184 + 1 )
= ( 9.2 )8 - [ ( 184 )2 - 12 ]
= 188 - 188 + 1
= 1
c) \(\frac{780^2-220^2}{125^2+150\cdot125+75^2}\)
\(=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2\cdot75\cdot125+75^2}\)
\(=\frac{560\cdot1000}{\left(125+75\right)^2}\)
\(=\frac{560000}{200^2}\)
\(=\frac{560000}{40000}=14\)
a) \(\dfrac{63^2-47^2}{215^2-105^2}\)
= \(\dfrac{\left(63-47\right)\left(63+47\right)}{\left(215-105\right)\left(215+105\right)}\)
= \(\dfrac{16.110}{110.320}=\dfrac{16}{320}=\dfrac{1}{20}\)
b) \(\dfrac{437^2-363^2}{537^2-463^2}\)
= \(\dfrac{\left(437-363\right)\left(437+363\right)}{\left(537-463\right)\left(537+463\right)}\)
= \(\dfrac{74.800}{74.1000}=\dfrac{800}{1000}=\dfrac{4}{5}\)
2)
A = \(26^2-24^2=\left(26-24\right)\left(26+24\right)=2.50=100\)
B = \(27^2-25^2=\left(27-25\right)\left(27+25\right)=2.52=104\)
Từ đó suy ra A < B
1.
\(a.\: \dfrac{63^2-47^2}{215^2-105^2}=\dfrac{\left(63-47\right)\left(63+47\right)}{\left(215-105\right)\left(215+105\right)}\\ =\dfrac{16.110}{110.320}=\dfrac{16}{320}=\dfrac{1}{20}\)
\(b.\dfrac{437^2-363^2}{537^2-463^2}=\dfrac{\left(437-363\right)\left(437+363\right)}{\left(537-463\right)\left(537+463\right)}\\ =\dfrac{74.800}{74.1000}=\dfrac{800}{1000}=\dfrac{4}{5}\)
2.
\(A=26^2-24^2=\left(26-24\right)\left(26+24\right)=2.50=100\)
\(B=27^2-25^2=\left(27-25\right)\left(27+25\right)=2.52=104\)
\(vì\:100< 104\:nên\:26^2-24^2< 27^2-25^2\\ hay\:A< B\)
1012
= (100 + 1)²
= 100² + 2.100.1 + 1²
= 10000 + 200 + 1
= 10201
a. 1012 = 10201
b. 97 x 103 = 9991
c. 772 + 232 + 77 x 46
= 5929 + 529 + 77 x 46
= 5929 + 529 + 3542
= 6458 + 3542
= 10000
d. 1052 - 5
= 11025 - 5
= 11020
Ta có:63^2-47^2=3969-2209=1760
215^2-105^2=46225-11025=35200
ks nhé!Học tốt!
Giải:
a) Sửa đề: 1272 + 146.127 + 732
\(127^2+146.127+73^2=\left(127+7\right)^2=200^2=40000\)
b) \(9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)=18^8-\left(18^4-1\right)^2=18^8-18^8-1=-1\)
c) \(20^2+18^2+16^2+...+4^2+2^2-\left(19^2+17^2+...+3^2+1\right)\)
\(=20^2+18^2+16^2+...+4^2+2^2-19^2-17^2-...-3^2-1\)
\(=\left(20^2-19^2\right)+\left(18^2-17^2\right)+\left(16^2-15^2\right)+...+\left(4^2-3^2\right)+\left(2^2-1\right)\)
\(=20+19+18+17+16+15+...+4+3+2+1\)
\(=\dfrac{\left(20+1\right).20}{2}=210\)
Chúc bạn học tốt!
a) 1012
= (100 + 1)2
= 1002 + 2.100 + 1
= 10000 + 200 + 1
= 10201
b) 97.103
= (100 - 3)(100 + 3)
= 1002 - 32
= 10000 - 9
= 9991
c) 772 + 232 + 77.46
= 772 + 2.77.23 + 232
= (77 + 23)2
= 1002
= 10000
d) 1052 - 52
= (105 - 5)(105 + 5)
= 100.110
= 11000
a) \(105^3-15.105^2+75.105-125\)
\(=105^3-3.105^2.5+3.105.5^2-5^3\)
\(=\left(105-5\right)^3\)
\(=100^3=1000000\)
b) \(63^2-27^2+72^2-18^2\)
\(=\left(63-27\right)\left(63+27\right)+\left(72-18\right)\left(72+18\right)\)
\(=36.90+54.90\)
\(=90.90=8100\)
A= 1000000
B=8100