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1. xy + 5x + 5y = 92
=> (xy + 5x) + (5y + 25) = 92 + 25
=> x(y + 5) + 5(y + 5) = 117
=> (x + 5)(y + 5) = 117
=> x + 5 \(\in\)Ư(117) = {-1;1;-3;3;-9;9;-13;13;-39;39;-117;117}
Mà x >= 0 => x + 5 >= 5
=> x + 5 \(\in\){9;13;39;117}
Ta có bảng sau:
x + 5 | 9 | 13 | 39 | 117 |
x | 4 | 8 | 34 | 112 |
y + 5 | 13 | 9 | 3 | 1 |
y | 8 | 4 | -2 (loại) | -4 (loại) |
Vậy; (x;y) \(\in\){(4;8);(8;4)}
2:
1: =>36x+14x=69+81=150
=>50x=150
=>x=3
2: 3^x=81
=>3^x=3^4
=>x=4
3: 3(2x+1)^2=75
=>(2x+1)^2=25
=>2x+1=5 hoặc 2x+1=-5
=>x=-3 hoặc x=2
1:
1: \(\dfrac{13\cdot17^4+4\cdot17^4}{17^3}-\dfrac{14\cdot3^3-14\cdot3^2}{9}\)
\(=\dfrac{17^4\cdot\left(13+4\right)}{17^3}-\dfrac{14\cdot3^2\left(3-1\right)}{9}\)
\(=17\cdot17-14\cdot2\)
=289-28
=261
2:
\(2^3\cdot5^2-\left[131-\left(23-2^3\right)^2\right]\)
\(=8\cdot25-131+\left(-1\right)^2\)
=69+1
=70
3.4x-2+4x-1+4x=92
3.4x-2+4x-2+1+4x--2+2=92
3.4x-2+4x-2.4+4x-2.16=92
4x-2.(3+4+16)=92
4x-2.23=92
4x-2=92:23
4x-2=4
=>x-2=1
x=3
vay...
\(3.4^{x-2}+4^{x-1}+4^x=92\)\
<=> \(\frac{3}{16}.4^x+\frac{1}{4}.4^x+4^x=92\)
<=> \(\left(\frac{3}{16}+\frac{1}{4}+1\right).4^x=92\)
<=> \(\frac{23}{16}.4^x=92\)
<=> \(4^x=64\)
<=> x = 3
3.4^x-2+4^x-1+4^x=92
12^x-2+4^x-1+4^x=92
4(3^x-2+1^x-1+1^x)=92
4(3^x-2+2)=92
3^x-2+2=23
3^x-2=21
3^x-2=3.7
=>x-2=1
x=3
\(a,x-36:18=12-15\\ \Rightarrow x-2=-3\\ \Rightarrow x=-1\\ b,92-\left(17+x\right)=72\\ \Rightarrow17+x=20\\ \Rightarrow x=3\\ c,720:\left[41-\left(2x+5\right)\right]=40\\ \Rightarrow41-\left(2x+5\right)=18\\ \Rightarrow2x+5=23\\ \Rightarrow2x=18\\ \Rightarrow x=9\\ d,\left(x+2\right)^3-23=41\\ \Rightarrow\left(x+2\right)^3=64\\ \Rightarrow\left(x+2\right)^3=4^3\\ \Rightarrow x+2=4\\ \Rightarrow x=2\)
92-2x=2(x+4)
92-2x=2x+8=8+2x
92-2x-2x=8
92-4x=8
4X=92-8
4x=84
X=84:4=21
92 - 2x = 2 . ( x + 4 )
92 - 2x = 2x + 2 . 4
92 - 2x = 2x + 8
2x - 2x = 92 + 8
2x = 100
x = 100 : 2
x = 50
Vẫy x = 50