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-4.|x-1| + (1/2-2,5)2 = -3
-4.|x-1| + (-2)2 = -3
-4.|x-1| + 4 = -3
-4.|x-1| = -3 - 4
-4.|x-1| = -7
|x-1| = (-7) : (-4)
|x-1| = 7/4
TH1: x - 1 = 7/4 => x = 7/4 + 1 = 11/4
TH2: 1 - x = 7/4 => x = 1 - 7/4 = -3/4
Vậy x = {11/4; -3/4}
\(a,\frac{62}{7}:x=\frac{29}{9}:\frac{3}{56}\)
\(\frac{62}{7}:x=\frac{1624}{27}\)
\(x=\frac{62}{7}:\frac{1624}{27}=\frac{837}{5684}\)
\(b,\frac{1}{5}:x=\frac{1}{5}-\frac{1}{7}\)
\(\frac{1}{5}:x=\frac{2}{35}\)
\(x=\frac{1}{5}:\frac{2}{35}=\frac{7}{2}\)
\(c,\frac{2}{3}.x-\frac{4}{7}=\frac{1}{7}\)
\(\frac{2}{3}.x=\frac{1}{7}+\frac{4}{7}=\frac{5}{7}\)
\(x=\frac{5}{7}:\frac{2}{3}=\frac{15}{14}\)
\(d,\frac{2}{7}-\frac{8}{9}.x=\frac{2}{3}\)
\(\frac{8}{9}.x=\frac{2}{7}-\frac{2}{3}=-\frac{8}{21}\)
\(x=-\frac{8}{21}:\frac{8}{9}=-\frac{3}{7}\)
\(e,\frac{4}{7}+\frac{5}{9}:x=\frac{1}{5}\)
\(\frac{5}{9}:x=\frac{1}{5}-\frac{4}{7}=-\frac{13}{35}\)
\(x=\frac{5}{9}:-\frac{13}{35}=\frac{175}{117}\)
\(i,\frac{2}{5}-\frac{2}{5}.x=\frac{2}{5}\)
\(\frac{2}{5}.\left(1-x\right)=\frac{2}{5}\)
\(1-x=\frac{2}{5}:\frac{2}{5}=1\)
\(x=1-1=0\)
\(g,\frac{2}{3}+\frac{1}{3}:x=-1\)
\(\frac{1}{3}:x=-1-\frac{2}{3}=-\frac{5}{3}\)
\(x=\frac{1}{3}:-\frac{5}{3}=-\frac{1}{5}\)
học tốt nha
a) xy - 5y = 13
y . ( x - 5 ) = 13
Lập bảng ta có :
| x-5 | 13 | 1 | -13 | -1 |
| x | 18 | 6 | -8 | 4 |
| y | 1 | 13 | -1 | -13 |
Vậy ( x ; y ) = ( 18 ; 1 ) = ( 6 ; 13 ) = ( -8 ; -1 ) = ( 4 ; -13 )
# Chúc bạn học tốt ^^!
a) xy - 5y = 13
y . ( x - 5 ) = 13
Lập bảng ta có :
| x-5 | 13 | 1 | -13 | -1 |
| x | 18 | 6 | -8 | 4 |
| y | 1 | 13 | -1 | -13 |
Vậy ( x ; y ) = ( 18 ; 1 ) = ( 6 ; 13 ) = ( -8 ; -1 ) = ( 4 ; -13 )
Ta có: \(\frac{x+2}{3}=\frac{y-1}{4}=\frac{z+5}{7}\)
\(\Rightarrow\frac{2\left(x+2\right)}{6}=\frac{y-1}{4}=\frac{z+5}{7}\)
\(\Rightarrow\frac{2x+4}{6}=\frac{y-1}{4}=\frac{z+5}{7}\)
Áp dụng tính chất dãy tỉ số bằng nhau được:
\(\frac{2x+4-\left(y-1\right)+z+5}{6-4+7}=\frac{2x+4-y+1+z+5}{6-4+7}=\frac{\left(2x-y+z\right)+\left(4+1+5\right)}{6-4+7}\)
\(=\frac{17+10}{9}=\frac{27}{9}=3\)
Suy ra: \(2x+4=6.3\Rightarrow2x=14\Rightarrow x=7\)
\(y-1=3.4\Rightarrow y=13\)
\(z+5=3.7\Rightarrow z=16\)
Vậy x = 7 ; y = 13; z = 16
3/4+1/4:x=-3
1/4:x=(-3)-3/4
1/4:x=-15/4
x=-15/4.1/4
x=-15/16
đúng nha bn
\(2^x:1+2^x:2+...+2^x:49=2^{49}-1\)
\(2^x.1+2^x.\frac{1}{2}+...+2^x.\frac{1}{49}=2^{49}-1\)
\(2^x.\left(1+\frac{1}{2}+...+\frac{1}{49}\right)=2^{49}-1\)
Đặt: \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}\)
=> \(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^{49}}\right)\)
=> \(A=1-\frac{1}{2^{49}}=\frac{2^{49}-1}{2^{49}}\)
\(2^{x-1}+2^{x-2}+2^{x-3}+...+2^{x-49}=2^{49}-1\)
<=> \(\frac{2^x}{2}+\frac{2^x}{2^2}+\frac{2^x}{2^3}+...+\frac{2^x}{2^{49}}=2^{49}-1\)
<=> \(2^x\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}\right)=2^{49}-1\)
<=> \(2^x.\frac{2^{49}-1}{2^{49}}=2^{49}-1\)
<=> \(2^x=2^{49}\)
<=> x = 49.
Lời giải:
a. $9x^2-16-(3x-4)(2x+5)=0$
$\Leftrightarrow [(3x)^2-4^2]-(3x-4)(2x+5)=0$
$\Leftrightarrow (3x-4)(3x+4)-(3x-4)(2x+5)=0$
$\Leftrightarrow (3x-4)(3x+4-2x-5)=0$
$\Leftrightarrow (3x-4)(x-1)=0$
$\Leftrightarrow 3x-4=0$ hoặc $x-1=0$
$\Leftrightarrow x=\frac{4}{3}$ hoặc $x=1$.
b.
$x^2+4x=12$
$\Leftrightarrow x^2+4x-12=0$
$\Leftrightarrow (x^2-2x)+(6x-12)=0$
$\Leftrightarrow x(x-2)+6(x-2)=0$
$\Leftrightarrow (x-2)(x+6)=0$
$\Leftrightarrow x-2=0$ hoặc $x+6=0$
$\Leftrightarrow x=2$ hoặc $x=-6$
c.
$x^2-2x=35$
$\Leftrightarrow x^2-2x-35=0$
$\Leftrightarrow (x^2+5x)-(7x+35)=0$
$\Leftrightarrow x(x+5)-7(x+5)=0$
$\Leftrightarrow (x+5)(x-7)=0$
$\Leftrightarrow x+5=0$ hoặc $x-7=0$
$\Leftrightarrow x=-5$ hoặc $x=7$
\(\left(4x-1\right)^3=\frac{-1}{27}\)
\(\Rightarrow\left(4x-1\right)^3=\left(\frac{-1}{3}\right)^3\)
\(\Rightarrow4x-1=\frac{-1}{3}\)
\(\Rightarrow4x=\frac{-1}{3}+1\)
\(\Rightarrow4x=\frac{2}{3}\)
\(\Rightarrow x=\frac{2}{3}:4\)
\(\Rightarrow x=\frac{1}{6}\)