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22.23=(20+2).23=460+46=506
44.101=44(100+1)=4400+44=4444
25.105=25(100+5)=250+125=375
1052 - 25 = 1052 - 52
= (105 + 5)(105 - 5)
= 110.100
= 11000
15 . 64 + 25 . 100 + 36 . 15 + 60 . 100
= (15 . 64 + 36 . 15) + (25 . 100 + 60 . 100)
= 15. (64 + 36) + 100. (25 + 60)
= 15 . 100 + 100 . 85
= 100 . (15 + 85)
= 100 . 100
= 10000
a) \(103^2=\left(100+3\right)^2=10000+600+9=10609\)
b) \(52\cdot48=\left(50-2\right)\left(50+2\right)=2500-4=2496\)
c) \(75^2-50\cdot75+25^2=\left(75-25\right)^2=50^2=2500\)
\(103^2=\left(100+3\right)^2=100^2+2.3.100+3^2=10000+600+9=10609\)
\(52.48=\left(50+2\right)\left(50-2\right)=50^2-2^2=2500-4=2496\)
\(75^2-50.75+25^2=75^2-25.75-25.75+25^2=75\left(75-25\right)-25\left(75-25\right)=\left(75-25\right)=50^2=2500\)
\(=\left(57^2-43^2\right)+\left(75^2-25^2\right)\\ =\left(57-43\right)\left(57+43\right)+\left(75-25\right)\left(75+25\right)\\ =100\cdot14+100\cdot50\\ =100\left(50+14\right)\\ =100\cdot64=6400\)
=15.(64+36)+100.(25+60)
=15.100+85.100
=100.(15+85)
=100.100
=10000
= 52 - 2.5.x + x2 = (5 - x)2
Thay x=15: (5-15)2 = 102 = 100
Ta có : x2 - 2x + 1 = 25
=> x2 - 2.x.1 + 12 = 25
=> (x - 1)2 = 25
Mà 25 = 52 ; (-5)2
=> \(\orbr{\begin{cases}\left(x-1\right)^2=5^2\\\left(x-1\right)^2=\left(-5\right)^2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-1=5\\x-1=-5\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}\)
Vậy x = {-4;6}
b) (5 - 2x)2 + 1 = 25
<=> (5 - 2x)2 = 24
\(\Rightarrow\orbr{\begin{cases}5-2x=\sqrt{24}\\5-2x=-\sqrt{24}\end{cases}}\Rightarrow\orbr{\begin{cases}2x=5-2\sqrt{6}\\2x=5+2\sqrt{6}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{5-2\sqrt{6}}{2}\\x=\frac{5+2\sqrt{6}}{2}\end{cases}}\)
25 . 4=100
cj bb^^
\(25+25+25+25=25\cdot4=200\)
Aj k mk mk k lại ckoa!^^