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i) \(2345-1000\div\left[19-2\left(21-18\right)^2\right]\)
\(=\)\(2345-1000\div\left[19-2.3^2\right]\)
\(=\)\(2345-1000\div\left[19-2.9\right]\)
\(=\)\(2345-1000\div\left[19-18\right]\)
\(=\)\(2345-1000\div1\)
\(=\)\(2345-1000\)
\(=\)\(1345\)
j) \(128-\left[68+8\left(37-35\right)^2\right]\div4\)
\(=\)\(128-\left[68+8.2^2\right]\div4\)
\(=\)\(128-\left[68+8.4\right]\div4\)
\(=\)\(128-\left[68+32\right]\div4\)
\(=\)\(128-100\div4\)
\(=\)\(128-25\)
\(=\)\(3\)
k) \(568-\left\{5\left[143-\left(4-1\right)^2\right]+10\right\}\div10\)
\(=\)\(568-\left\{5\left[143-3^2\right]+10\right\}\div10\)
\(=\)\(568-\left\{5\left[143-9\right]+10\right\}\div10\)
\(=\)\(568-\left\{5.134+10\right\}\div10\)
\(=\)\(568-\left\{670+10\right\}\div10\)
\(=\)\(568-680\div10\)
\(=\)\(568-68\)
\(=\)\(500\)
a) \(107-\left\{38+\left[7.3^2-24\div6+\left(9-7\right)^3\right]\right\}\div15\)
\(=\)\(107-\left\{38+\left[7.3^2-24\div6+2^3\right]\right\}\div15\)
\(=\)\(107-\left\{38+\left[7.9-4+8\right]\right\}\div15\)
\(=\)\(107-\left\{38+\left[63-4+8\right]\right\}\div15\)
\(=\)\(107-\left\{38+67\right\}\div15\)
\(=\)\(107-105\div15\)
\(=\)\(107-7\)
\(=\)\(7\)
b) \(307-\left[\left(180-160\right)\div2^2+9\right]\div2\)
\(=\)\(307-\left[20\div4+9\right]\div2\)
\(=\)\(307-\left[5+9\right]\div2\)
\(=\)\(307-14\div2\)
\(=\)\(307-7\)
\(=\)\(300\)
c) \(205-\left[1200-\left(4^2-2.3\right)^3\right]\div40\)
\(=\)\(205-\left[1200-\left(16-6\right)^3\right]\div40\)
\(=\)\(205-\left[1200-10^3\right]\div40\)
\(=\)\(205-\left[1200-1000\right]\div40\)
\(=\)\(205-200\div40\)
\(=\)\(205-5\)
\(=\)\(200\)
Answer:
a)
Có:
\(15=1.15=\left(-1\right).\left(-15\right)=3.5=\left(-3\right).\left(-5\right)\)
| x-3 | 1 | 15 | -1 | -15 | 3 | 5 | -3 | -5 |
| y+1 | 15 | 1 | -15 | -1 | 5 | 3 | -5 | -3 |
| x | 4 | 18 | 2 | -12 | 6 | 8 | 0 | -2 |
| y | 14 | 0 | -16 | -2 | 4 | 2 | -6 | -4 |
b)
Có:
\(M=1+3+3^2+3^3+3^4+...+3^{98}+3^{99}+3^{100}\)
\(=\left(1+3\right)+\left(3^2+3^3+3^4\right)+...+\left(3^{98}+3^{99}+3^{100}\right)\)
\(=4+3^2.\left(1+3+3^2\right)+...+3^{98}.\left(1+3+3^2\right)\)
\(=4+3^2.13+3^{98}.13\)
\(=4+13.\left(3^2+...+3^{98}\right)\)
Vậy M chia 13 dư 4
Có:
\(M=1+3+3^2+3^3+3^4+...+3^{99}+3^{100}\)
\(=1+\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)
\(=1+3.40+3^5.40+...+3^{97}.40\)
\(=1+40.\left(3+3^5+...+3^{97}\right)⋮40\)
Mà \(40\left(3+3^5+...+3^{97}\right)⋮40\)
Vậy M chia 40 dư 1
a) 15 + 23 = 1 + 8 = 9 = 32 ( là số chính phương )
b) 52 + 122 = 25 + 144 = 169 = 132 ( là số chính phương )
c) 26 + 62 = 64 + 36 = 100 = 1002 ( là số chính phương )
d) 13 + 23 + 33 + 43 + 53 + 63
= 1 + 8 + 27 + 64 + 125 + 216
= 441 = 212 ( là số chính phương )
a) 15 + 23=1 + 8 = 9 (là số chính phương)
b) 52 + 122= 25 + 144= 169 (là số chính phương)
c) 26 + 62= 64 + 36=100 (là số chính phương)
d) 142 – 122= 196 - 144=52 (không là số chính phương)
e) 13 + 23 + 33 + 43 + 53 + 63= 1 + 8 + 27 + 64 + 125 + 216 = 411 (là số chính phương)
d) 135 - 5(x+4) = 35
5(x+4) = 100
x+4 = 20
x = 16
e) 25 + 3(x-8)=106
3(x-8) = 81
x-8=27
x=35
a) 2(x - 51) = 2.23 + 20
2(x - 51) = 16 + 20
2(x - 51) = 36
x - 51 = 36 : 2
x - 51 = 18
x = 18 + 51
x = 69
b) 450 : (x - 19) = 50
x - 19 = 50.450
x - 19 = 22500
x = 22500 + 19
x = 22519
c) 4(x - 3) = 72 - 110
4(x - 3) = 49 - 1
4(x - 3) = 48
x - 3 = 48 : 4
x - 3 = 12
x = 12 + 3
x = 15
d) 135 - 5(x + 4) = 35
-5(x + 4) = 35 - 135
-5(x + 4) = -100
x + 4 = (-100) : (-5)
x + 4 = 20
x = 20 - 4
x = 16
e) 25 + 3(x - 8) = 106
3(x - 8) = 106 - 25
3(x - 8) = 81
x - 8 = 81 : 3
x - 8 = 27
x = 27 + 8
x = 35
f) 32(x + 4) - 52 = 5.22
9(x + 4) - 25 = 20
9(x + 4) = 20 + 25
9(x + 4) = 45
x + 4 = 45 : 9
x + 4 = 5
x = 5 - 4
x = 1
a) \(2\left(x-51\right)=2.2^3+20\)
\(\Leftrightarrow2\left(x-51\right)=16+20\)
\(\Leftrightarrow2\left(x-51\right)=36\)
\(\Leftrightarrow x-51=36:2\)
\(\Leftrightarrow x-51=18\)
\(\Leftrightarrow x=69\)
a,\(2.\left(x-51\right)=2.2^3+20\)
\(=>2.\left(x-51\right)=2.\left(2^3+10\right)\)
\(=>x-51=8+10=18\)
\(=>x=18+51=69\)
b,\(450:\left(x-19\right)=50\)
\(=>x-19=\frac{450}{50}=9\)
\(=>x=9+19=28\)
c,\(4.\left(x-3\right)=7^2-1^{10}\)
\(=>4x-12=49-1=48\)
\(=>4x=48+12=60\)
\(=>x=\frac{60}{4}=15\)
d,\(135-5.\left(x+4\right)=35\)
\(=>5.\left(x+4\right)=135-35=100\)
\(=>5.\left(x+4\right)=5.20\)
\(=>x+4=20\)
\(=>x=20-4=16\)
e,\(25+3.\left(x-8\right)=106\)
\(=>3.\left(x-8\right)=25-106=-81\)
\(=>3.\left(x-8\right)=3.\left(-27\right)\)
\(=>x-8=-27\)
\(=>x=-27+8=-19\)