108 - 3 [2x + 12] =42
Quy đồng các số sau: -3/7 và 5/9 -42/108 và 5/12
a: -3/7=-27/63
5/9=35/63
b: -42/108=-7/12
5/12=5/12
Điền vào dấu ? (Quy luật)
4, 6, 12, 18, 30, 42, 60, 72, 102, 108, ?, ?
\(\dfrac{x^2+2x}{2x+12}+\dfrac{x-6}{x}+\dfrac{108-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x^3+2x^2+2x^2-72+108-6x}{2x\left(x+6\right)}\\ =\dfrac{x^3+6x^2-2x^2-12x+6x+36}{2x\left(x+6\right)}\\ =\dfrac{\left(x+6\right)\left(x^2-2x+6\right)}{2x\left(x+6\right)}=\dfrac{x^2-2x+6}{2x}\)
\(\dfrac{x^2+2x}{2x+12}+\dfrac{x-6}{x}+\dfrac{108-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x^2+2x}{2\left(x+6\right)}+\dfrac{x-6}{x}+\dfrac{108-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x\left(x^2+2x\right)+2\left(x+6\right)\left(x-6\right)+108-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x^3+2x^2+2\left(x^2-36\right)+108-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x^3+2x^2+2x^2-72+108-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x^3+4x^2+36-6x}{2x\left(x+6\right)}\)
\(=\dfrac{x^3+6x^2-2x^2-12x+6x+36}{2x\left(x+6\right)}\)
\(=\dfrac{\left(x^3+6x^2\right)+\left(-2x^2-12x\right)+\left(6x+36\right)}{2x\left(x+6\right)}\)
\(=\dfrac{x^2\left(x+6\right)-2x\left(x+6\right)+6\left(x+6\right)}{2x\left(x+6\right)}\)
\(=\dfrac{\left(x+6\right)\left(x^2-2x+6\right)}{2x\left(x+6\right)}\)
\(=\dfrac{x^2-2x+6}{2x}\)
Tính giá trị biểu thức
A=1/4+1/12+1/36+1/108+1/324+1/972
B=1/2+5/6+11/12+19/20+29/30+41/42+55/56
\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)
\(3A=3\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right)\)
\(3A=\frac{3}{4}+\frac{3}{12}+\frac{3}{36}+\frac{3}{108}+\frac{3}{324}+\frac{3}{927}\)
\(3A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)
\(2A=3A-A\)
\(2A=\left(\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\right)-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right)\)
\(2A=\frac{3}{4}-\frac{1}{927}\)
\(2A=\frac{729-1}{972}=\frac{728}{972}=\frac{182}{243}\)
\(A=\frac{182}{243}:\frac{1}{2}\)
\(A=\frac{364}{243}\)
A=1/4+1/12+1/36+1/108+1/324+1/972
=243/972+81/972+27/972+9/972+3/972+1/972
=364/972
=91/243
\(B=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}\)
\(B=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{30}\right)+\left(1-\frac{1}{42}\right)+\left(1-\frac{1}{56}\right)\)
\(B=1.9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}\right)\)
\(B=9-\left[\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{56}\right)\right]\)
\(B=9-\left(1-\frac{1}{56}\right)\)
\(B=9-\frac{55}{56}\)
\(B=\frac{449}{56}\)
a) 42-x=5
b) 15.(x+4)=75
c) 27+3x=9^8.9^7
d) x+18=12
e) 2x-15=-19
f) 36 :(x^3-12)=-3
g)x+15=35
h) 2x-13=3^2
a) 42 - x = 5
x = 42 - 5
x = 37
b) 15.(x + 4) = 75
x + 4 = 75 : 15
x + 4 = 5
x = 5 - 4
x = 1
d) x + 18 = 12
x = 12 - 18
x = -6
e) 2x - 15 = -19
2x = (-19) + 15
2x = -4
x = -4 : 2
x = -2
f) 36 : (x^3 - 12) = -3
x^3 - 12 = 36 : (-3)
x^3 - 12 = -12
x^3 = 0
=> x = 0
g)x + 15 = 35
x = 35 - 15
x = 20
h) 2x - 13 = 3^2
2x - 13 = 9
2x = 9 + 13
2x = 22
x = 22 : 2
x = 11
a) 42-x=5
x=42-5
x= 37
b)15*(x+4)=75
x+4=75:15
x+4=5
x =5-4
x = 1
a) 42 - x = 5
x = 42 - 5
x = 37
b) 15.(x + 4) = 75
x + 4 = 75 : 15
x + 4 = 5
x = 5 - 4
x = 1
d) x + 18 = 12
x = 12 - 18
x = -6
e) 2x - 15 = -19
2x = (-19) + 15
2x = -4
x = -4 : 2
x = -2
f) 36 : (x^3 - 12) = -3
x^3 - 12 = 36 : (-3)
x^3 - 12 = -12
x^3 = 0
=> x = 0
g)x + 15 = 35
x = 35 - 15
x = 20
h) 2x - 13 = 3^2
2x - 13 = 9
2x = 9 + 13
2x = 22
x = 22 : 2
x = 11
Giải các phương trình sau:
a) 3 x − 3 + 2 x + 1 2 − x + 4 2 = 0 ;
b) 2 x − 5 2 x − 3 8 + 1 = x − 5 2 2 x − 3 8 + 1 .
2/3 + 3/18 + 1/42 + 2/63 + 3/108 = ...
Mik cần gấp, cảm ơn mn ạ!!
A = \(\dfrac{2}{3}\) + \(\dfrac{3}{18}\) + \(\dfrac{1}{42}\) + \(\dfrac{2}{63}\) + \(\dfrac{3}{108}\)
A = \(\dfrac{2}{1\times3}\) + \(\dfrac{3}{3\times6}\) + \(\dfrac{1}{6\times7}\)+ \(\dfrac{2}{7\times9}\) + \(\dfrac{3}{9\times12}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{12}\)
A = 1 - \(\dfrac{1}{12}\)
A = \(\dfrac{11}{12}\)
A, (x-4)(x-5)=12
B,(2x-2)(2x-4)=3
C,(x-5)(x+6)=42
D, (2x-1)(x+3)=-6
a) \(⇔x^2-9x+20=12 \)
\(⇔x^2-9x+8=0\)
\(⇔x^2-x-8x+8=0\)
\(⇔(x-1)(x-8)=0\)
\(⇔\left[\begin{array}{} x-1=0\\ x-8=0 \end{array}\right.⇔\left[\begin{array}{} x=1\\ x=8 \end{array}\right.\)
b) \(⇔4x^2-12x+8=3\)
\(⇔4x^2-12x+5=0\)
\(⇔(2x-1)(2x-5)=0\)
\(⇔\left[\begin{array}{} 2x-1=0\\ 2x-5=0 \end{array}\right.⇔\left[\begin{array}{} x=\frac{1}{2}\\ x=\frac{5}{2} \end{array}\right.\)
c) \(⇔x^2+x-30=42\)
\(⇔x^2+x-72=0\)
\(⇔(x-9)(x+8)=0\)
\(⇔\left[\begin{array}{} x-9=0\\ x+8=0 \end{array}\right.⇔\left[\begin{array}{} x=9\\ x=-8 \end{array}\right.\)
d) \(⇔2x^2+5x-3=-6\)
\(⇔2x^2+5x+3=0\)
\(⇔(x+1)(2x+3)=0\)
\(⇔\left[\begin{array}{} x+1=0\\ 2x+3=0 \end{array}\right.⇔\left[\begin{array}{} x=-1\\ x=-\frac{3}{2} \end{array}\right.\)
A, (x-4)(x-5)=12
B,(2x-2)(2x-4)=3
C,(x-5)(x+6)=42
D, (2x-1)(x+3)=-6
Đề bài là j vậy bạn?