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\(e,112-45+5x=87\)
\(67+5x=87\)
\(5x=20\)
\(x=4\)
\(f,6^2+64:\left(x-1\right)=52\)
\(36+64:\left(x+1\right)=52\)
\(64:\left(x+1\right)=16\)
\(x+1=4\)
\(x=3\)
a, 5x = 201 - 6 = 195
x = 195 : 5 = 39
b, 135 - 2x = 87
2x = 135 - 87 = 48
x = 48 : 2 = 24
c, 45 - ( x - 17 ) : 3 = 38
( x - 17 ) : 3 = 45 - 38 =7
x - 17 = 7 . 3 = 21
x = 21 + 17 = 38
1. Thực hiện phép tính bằng cách hợp lí :
a) (-46) + (-125) + 46 + 25 = [(-46)+46] + [(-125)+25]
= 0+(-100) = -100
b) 25.(-15) + 25.(-5) + (-20).75 = 25.[(-15)+(-5)] + (-20).75
= 25.(-20) + (-20).75 = (-20).(25+75) = (-20).100 = -2000
c) (-151)+(-37)+(-42)+(-63)+142 =(-151)+[(-37)+(-63)]+[(-42)+142]
= (-151) + [(-100) + 100] = -151
d)32+(-149)+(-311)+(-89)+(-51) = 32+[(-149)+(-51)] + [(-311)+(-89)]
= 32+[(-200)+(-400)] = 32+(-600) = -568
e)-65.(87-17)-87.(17-65) = (-65).87 - (-65).17 - 87.17 + 87.65
= (-65).87 + 65.17 - 87.17 + 87.65 = [(-65).87+87.65] + 65.(17-87)
= 65.(-70) = -4550
g) -43.(53-16) - 53.(16-43) = (-43).53 - (-43).16 - 53.16 + 53.43
= (-43).53 + 43.16 - 53.16 + 53.43 = [(-43).53+53.43] + 16.(43-53)
= 16.(-10) = -160
Ta có: \(A=1.3+2.4+3.5+4.6+...+99.101+100.102\)
\(A=1.\left(1+2\right)+2.\left(2+2\right)+3.\left(3+2\right)+4.\left(4+2\right)+....+99.\left(99+2\right)+100.\left(100+2\right)\)
\(A=\left(1^2+2^2+3^2+4^2+...+99^2+100^2\right)+\left(2+4+6+8+...+198+200\right)\)Đặt \(B=1^2+2^2+3^2+4^2+5^2+...+99^2+100^2\)
\(\Rightarrow B=\left(1^2+2^2+3^2+4^2+5^2+...+99^2+100^2\right)-2^2.\left(1^2+2^2+3^2+4^2+5^2+....+49^2+50^2\right)\)Tính dãy tổng quát \(C=1^2+2^2+3^2+4^2+5^2+...+n^2\)
\(C=1\left(0+1\right)+2\left(1+1\right)+3.\left(2+1\right)+4.\left(3+1\right)+5\left(4+1\right)+...+n\left[\left(n-1\right)+1\right]\)
\(C=\left[1.2+2.3+3.4+4.5+...+\left(n-1\right).n\right]+\left(1+2+3+4+5+....+n\right)\)
\(C=n.\left(n+1\right).\left[\left(n-1\right):3+1:2\right]=n.\left(n+1\right).\left(2n+1\right):6\)
Áp dụng vào B ta được:
\(B=100.101.201:6-4.50.51.101:6=166650\)
\(\Rightarrow A=166650+\left(200+2\right).100:2\)
\(\Rightarrow A=166650+10100=176750\)
Vậy A = 176750
Chúc bạn học tốt!!
a)(2x+7)-25=14
2x+7 =14 +25
2x+7 =39
2x =39-7
2x =32
x =32:2
x =16
b) 87-(312-x):5=3.52
87-(312-x):5=156
87-(312-x) =156.5
87-(312-x) =780
312-x =87-780
312-x =-693
x = 312-(-693)
x =-381
c)3??? Viết lại đề nhé!
\(a,x=3x^2\Rightarrow x-3x^2=0\Rightarrow x\left(1-3x\right)=0\Rightarrow\orbr{\begin{cases}x=0\\1-3x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{1}{3}\end{cases}}\)
\(b,\left(2x-6\right)\left(x+4\right)+2\left(2x-6\right)=0\)
\(\Rightarrow\left(2x-6\right)\left(x+4+2\right)=0\)
\(\Rightarrow\left(2x-6\right)\left(x+6\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-6=0\\x+6=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=3\\x=-6\end{cases}}\)
\(c,\left(2x-5\right)\left(x+9\right)+6x-15=0\)
\(\Rightarrow\left(2x-5\right)\left(x+9\right)+3\left(2x-5\right)=0\)
\(\Rightarrow\left(2x-5\right)\left(x+9+3\right)=0\)
\(\Rightarrow\left(2x-5\right)\left(x+12\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-5=0\\x+12=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=-12\end{cases}}\)
a) \(\left(2x+3\right)^3=\left(2x+3\right)^8\)
TH1 \(2x+3=1\)
\(2x=1-3=-2\)
\(x=-1\)
TH2 \(2x+3=0\)
\(2x=-3\Rightarrow x=-\frac{3}{2}\)
b) ? sai đề
c) \(\left|5-3\right|=\left|11+2x\right|\Rightarrow\left|2\right|=\left|11+2x\right|\)
\(\hept{\begin{cases}11+2x=-2\\11+2x=2\end{cases}\Rightarrow}\hept{\begin{cases}2x=13\\2x=9\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{13}{2}\\x=\frac{9}{2}\end{cases}}\)
d) \(\left(x-5\right)^4=\left(x-5\right)^6\Rightarrow\hept{\begin{cases}x-5=0\\x-5=1\end{cases}}\Rightarrow\hept{\begin{cases}x=5\\x=6\end{cases}}\)
Phá ngoặc:
-12x +3 = 87
12x = - 84
x=-7
-2.(\(x\) + 6) + 5.(3 - 2\(x\)) = 87
-2\(x\) - 12 + 15 - 10\(x\) = 87
-(2\(x\) + 10\(x\)) + (15 - 12) = 87
-12\(x\) + 3 = 87
3 - 87 = 12\(x\)
12\(x\) = -84
\(x\) = -84 : 12
\(x\) = -7