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1) x - 36 + 12 = - x+ 10
=> x + x = 10 + 24
=> 2x = 34
=> x = 34/2 = 17
2) (x + 15) - (11 - x) = (-2)2
=> x + 15 - 11 + x = 4
=> 2x = 4 - 4
=> 2x = 0
=> x = 0
3) 40 - 4x2 = (-6)2
=> 40 - 4x2 = 36
=> 4x2 = 40 - 36
=> 4x2 = 4
=> x2 = 1
=> x = \(\pm\)1
4) (-50) + 10x2 = (-25) x |-2|
=> -50 + 10x2 = -50
=> 10x2 = -50 + 50
=> 10x2 = 0
=> x2 = 0
=> x = 0
5) |x + 1| = 2020
=> \(\orbr{\begin{cases}x+1=2020\\x+1=-2020\end{cases}}\)
=> \(\orbr{\begin{cases}x=2019\\x=-2021\end{cases}}\)
6) (x + 1)5 + 8 = 0 (xem lại đề)
7) (-20) + x3 : 16 = -24
=> x3 : 16 = -24 + 20
=> x3 : 16 = -4
=> x3 = -4 . 16
=> x3 = -64 = (-4)3
=> x = -4
9) x14 = x17
=> x14 - x17 = 0
=> x14(1 - x3) = 0
=> \(\orbr{\begin{cases}x^{14}=0\\1-x^3=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
10) (-36) + (1 - x)2 = 0
=> (1 - x)2 = 36
=> (1 - x)2 = 62
=> \(\orbr{\begin{cases}1-x=6\\1-x=-6\end{cases}}\)
=> \(\orbr{\begin{cases}x=-5\\x=7\end{cases}}\)
\(75-\left(3.5^2-4.2^3\right)\)
\(=75-3.25+4.8\)
\(=75-75+32\)
\(=32\)
\(72:\left[32+\left(100-2^2.17\right):8\right]\)
\(=72:\left[32+\left(100-4.17\right):8\right]\)
\(=72:\left[32+\left(100-68\right):8\right]\)
\(=72:\left(32+32:8\right)\)
\(=72:\left(32+4\right)\)
\(=72:36\)
\(=2\)
d)
\(152-3.\left\{\left[32-2\left(36\div x^2+7\right)\right]+42\right\}=-4\)
\(\Rightarrow3.\left\{\left[32-2\left(36\div x^2+7\right)\right]+42\right\}=152-\left(-4\right)\)
\(\Rightarrow3.\left\{\left[32-2\left(36\div x^2+7\right)\right]+42\right\}=156\)
\(\Rightarrow\left[32-2\left(36\div x^2+7\right)\right]+42=156\div3\)
\(\Rightarrow\left[32-2\left(36\div x^2+7\right)\right]+42=52\)
\(\Rightarrow32-2\left(36\div x^2+7\right)=52-42\)
\(\Rightarrow32-2\left(36\div x^2+7\right)=10\)
\(\Rightarrow2\left(36\div x^2+7\right)=32-10\)
\(\Rightarrow2\left(36\div x^2+7\right)=22\)
\(\Rightarrow36\div x^2+7=22\div2\)
\(\Rightarrow36\div x^2+7=11\)
\(\Rightarrow36\div x^2=11-7\)
\(\Rightarrow36\div x^2=4\)
\(\Rightarrow x^2=36\div4\)
\(\Rightarrow x^2=9\)
\(\Rightarrow x^2=3^2\)
\(\Rightarrow x=3\)
Vậy \(x=3\)
1. Tính giá trị biểu thức:
\(777:7+1331:11^3\)
\(=111+11^3:11^3\)
\(=111+1\)
\(=112\)
1.
\(777:7+1331:11^3=111+1331:1331=111+1=112\)
2.
\(2^{x+3}+2^x=36\\ 2^x\left(1+2^3\right)=36\\ 2^x\cdot9=36\\ 2^x=4\\ x=2\)
\(3^{x+4}+3^{x+2}=270\\ 3^{x+2}\cdot\left(3^2+1\right)=270\\ 3^{x+2}\cdot10=270\\ 3^{x+2}=27\\ x+2=3\\ x=1\)
\(\left(2x-5\right)^5=3^{10}\\ \left(2x-5\right)^5=3^{2\cdot5}\\ \left(2x-5\right)^5=\left(3^2\right)^5\\ \left(2x-5\right)^5=9^5\\ 2x-5=9\\ 2x=14\\ x=7\)
3.
\(31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}\\ 17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}>2^{55}\\ \Rightarrow31^{11}< 17^{14}\)
\(5^{300}=5^{2\cdot150}=\left(5^2\right)^{150}=25^{150}\\ 3^{453}=3^{3\cdot151}=\left(3^3\right)^{151}=27^{151}\\ 25^{150}< 25^{151}< 27^{151}\\ \Leftrightarrow5^{300}< 3^{453}\)
36 x 12 + 36 x 45 + 36 x 33
= 36 x (12 + 45 + 33)
= 36 x 90
= 3240
b) 78 x 31 + 78 x 24 + 78 x 17 + 22 x 72
=78 x (31 + 24 + 17) + 22 x 72
= 78 x 72 + 22 x 72
= (78 + 22) x 72
= 100 x 72
= 7200
c) ( 34 - 17 )2 - 23 x 32
\(=17^2-8.9\)
\(=289-72\)
\(=217\)