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a) \(5x-65=5.3^2 \\ 5x-65=45\\5x=45+65\\5x=110\\x=22\)
b) \(200-(2x+6)=4^3\\2x+6=200-4^3\\2x+6=136\\2x=130\\x=65\)
c) \(2(x-51)=2.2^3+20\\2(x-51)=16+20\\2(x-51)=36\\x-51=18\\x=51+18=69\)
d) \(135-5(x+4)=35\\5(x+4)=135-45\\5(x-4)=90\\x-4=18\\x=18+4=22\)
e) \((2x-4)(15-3x)=0\\2(x-2).3(5-x)=0\\(x-2)(5-x)=0\\ \left[ \begin{array}{l}x-2=0\\5-x=0\end{array} \right. \\ \left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)
f) \(2^{x+1} . 2^{2014}=2^{2016} \\ (2^{x+1} . 2^{2014}):2^{2014}=2^{2016} :2^{2014} \\ 2^{x=1}=2^{2016-2014} \\2^{x+1}=2^2\\x+1=2\\x=1\)
g) \(15+(x-1)^3=43\\(x-1)^3=15-42\\(x-1)^3=-27\\(x-1)^3=(-3)^3\\x-1=-3\\x=-2\)
h) \(15-x=17+(-9)\\15-x=17-9\\15-x=8\\x=15-8\\x=7\)
i) \(|x-5|=|-7|+|-4|\\|x-5|=7+4\\|x-5|=11\\ \left[ \begin{array}{l}x-5=11\\x-5=-11\end{array} \right. \\ \left[ \begin{array}{l}x=16\\x=-6\end{array} \right.\)
k) \(|x-3|-12=-9+|-7|\\|x-3|-12=-9+7\\|x-3|-12=-2\\|x-3|=10 \\ \left[ \begin{array}{l}x-3=10\\x-3=-10\end{array} \right. \\ \left[ \begin{array}{l}x=13\\x=-7\end{array} \right.\)
A.35 x 34 + 35 x 38 + 65 x 75 + 65 x 45
Câu này không tính hợp lí được
B. 12x 53 + 53 x 172 - 53 x 84
= 53 x (12 + 172 - 84)
= 53 x 100
= 5300
C. 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41
= 36 x (28+82) + 64 x (69+41)
= 36 x 110 + 64 x 110
= (36+64) x 110
= 100 x 110
= 11 000
D. A = 1+2+3+...+100
= (1+ 100) x 50
= 101 x 50
= 5050
E. B =17+19+...+101+103
= (103 +17) x [(103 - 17):2 + 1]
= 120 x 44
=5280
G. D= 3x (12+13+14+15) + 3x(8+7+6+5)
= 3 x (5+6+7+8+12+13+14+15)
= 3 x (20 x 4)
= 3 x 80
=240
15x35-3x(-5)x65=1500
\(15.35-3.\left(-5\right).65\)
\(=525+975\)
\(=1500\)