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\(\dfrac{2^2}{1\times3}\times\dfrac{3^2}{2.4}\times\dfrac{4^2}{3.5}\times\dfrac{5^2}{4.6}=\dfrac{2^2.3^2.4^2.5^2}{1.3.2.4.3.5.4.6}=\dfrac{2^2.3^2.4^2.5^2}{1.2.3.3.4.4.5.2.3}=\dfrac{2^2.3^2.4^2.5^2}{3^3.2^2.4^2.5.1}=\dfrac{5}{3.1}=\dfrac{5}{3}\)
\(\dfrac{2^2}{1\cdot3}\cdot\dfrac{3^2}{2\cdot4}\cdot\dfrac{4^2}{3\cdot5}\cdot\dfrac{5^2}{4.6}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot4\cdot6}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2}{1\cdot2\cdot4^2\cdot4^2\cdot5\cdot6}\\ =\dfrac{2\cdot5}{6}=\dfrac{5}{3}\)
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\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)
Đặt \(\left(1\right)=A\)
\(\Rightarrow A=1+5^2+...+5^{2x}\)
\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)
\(\Rightarrow24A=5^{2x+2}-1\)
\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)
Mà: \(A=\dfrac{25^6-1}{24}\)
\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)
\(\Rightarrow5^{2x+2}-1=5^{12}-1\)
\(\Rightarrow5^{2x+2}=5^{12}\)
\(\Rightarrow2x+2=12\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=\dfrac{10}{2}\)
\(\Rightarrow x=5\)
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a, 15 + x = 7
X= 7-15
x= -8
b, x - 9 = -24
x= -24+9
x= -15
c, - x + 8 = - 22
-x = -22-8
-x=-30
x=30
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1.2010 + 8 - 2010 - 22
=(2010 - 2010) + (8 - 22)
= 0 + -14
= -14
b..- ( - 98) - 99 + 12 + 99
=(98 + 12 ) + (99 - 99)
=110 + 0
=110
.3.1 + -123 + 7 - 8 + -123
=1 + (7 - 8) + [(-123) + (-123)]
= 1 + -1 + -246
=-246
4.72 - 24 - 37 + 24 + 37
=72 + (24 - 24) + (37 - 37)
=72 + 0 + 0
= 72
5.-90 - (-24 + 10) + 100
=-90 + 24 - 10 + 100
=[(-90) - 10] + 100 + 24
= -100 + 100 + 24
= 0 + 24
=24
1/ Thay x=2010 vào biểu thức,ta có:
2010+8-2010-22=-14
2/Thay x=-98 ;a=99 vào biểu thức,ta có:
-(-98)-99+12+99=98-99+12+99=110
3/Thay a=1 ;m=-123 vào biểu thức,ta có:
1-(-123)+7-8+(-123)=1+123+7-8+(-123)=0
Câu 4 và 5 tương tự