đưa về dạng tích:
a) x3 - 125
b) a3 + 27
c) -64 + \(\frac{1}{8}\)x3
d) 0,001 - 1000x3
e) (x +1)3 - (2 - x)3
f) \(\frac{1}{125}\)+ (x - \(\frac{1}{5}\))3
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5 tháng 10 2021
\(a,=8\left(x^3-125\right)=8\left(x-5\right)\left(x^2+5x+25\right)\\ b,=\left(0,1+4x\right)\left(0,01-0,4x+16x^2\right)\\ c,=\left(x+\dfrac{1}{5}y\right)\left(x^2-\dfrac{1}{5}xy+\dfrac{1}{25}y^2\right)\\ d,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ e,=\left(x-1+3\right)\left[\left(x-1\right)^2-3\left(x-1\right)+9\right]\\ =\left(x+2\right)\left(x^2-2x+1-3x+3+9\right)\\ =\left(x+2\right)\left(x^2-5x+13\right)\\ f,=\left(\dfrac{x^2}{2}-y^2\right)\left(\dfrac{x^4}{4}+\dfrac{x^2y^2}{2}+y^4\right)\)
S
19 tháng 3 2020
a) \(\left(-\frac{3}{4}\right)^{3x-1}=\frac{-27}{64}\)
\(\Leftrightarrow\left(-\frac{3}{4}\right)^{3x-1}=\left(-\frac{3}{4}\right)^3\)
\(\Leftrightarrow3x-1=3\)
\(\Leftrightarrow3x=4\)
\(\Leftrightarrow x=\frac{4}{3}\)
b) Đề sai ! Sửa :
\(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{625}\)
\(\Leftrightarrow\left(\frac{4}{5}\right)^{2x+5}=\left(\frac{4}{5}\right)^4\)
\(\Leftrightarrow2x+5=4\)
\(\Leftrightarrow2x=-1\)
\(\Leftrightarrow x=-\frac{1}{2}\)
c) \(\frac{\left(x+3\right)^5}{\left(x+5\right)^2}=\frac{64}{27}\)
\(\Leftrightarrow\left(x+3\right)^3=\left(\frac{4}{3}\right)^3\)
\(\Leftrightarrow x+3=\frac{4}{3}\)
\(\Leftrightarrow x=-\frac{5}{3}\)
d) \(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
\(\Leftrightarrow\left(x-\frac{2}{15}\right)^3=\left(\frac{2}{15}\right)^3\)
\(\Leftrightarrow x-\frac{2}{15}=\frac{2}{15}\)
\(\Leftrightarrow x=\frac{4}{15}\)
2 tháng 5 2020
a) Ta có: \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{7x}{8}-5x+45-\frac{20x+1,5}{6}=0\)
\(\Leftrightarrow\frac{21x}{24}-\frac{120x}{24}+\frac{1080}{24}-\frac{4\left(20x+1,5\right)}{24}=0\)
\(\Leftrightarrow-99x+1080-4\left(20x+1,5\right)=0\)
\(\Leftrightarrow-99x+1080-80x-6=0\)
\(\Leftrightarrow1074-179x=0\)
\(\Leftrightarrow179x=1074\)
hay x=6
Vậy: x=6
b) Ta có: \(4\left(0,5-1,5x\right)=-\frac{5x-6}{3}\)
\(\Leftrightarrow2-6x=\frac{6-5x}{3}\)
\(\Leftrightarrow\frac{3\left(2-6x\right)}{3}-\frac{6-5x}{3}=0\)
\(\Leftrightarrow6-18x-6+5x=0\)
\(\Leftrightarrow-13x=0\)
mà -13≠0
nên x=0
Vậy: x=0
c) Ta có: \(\frac{x+4}{5}-x+4=\frac{x}{3}-\frac{x-2}{2}\)
\(\Leftrightarrow\frac{6\left(x+4\right)}{30}+\frac{30\left(-x+4\right)}{30}-\frac{10x}{30}+\frac{15\left(x-2\right)}{30}=0\)
\(\Leftrightarrow6\left(x+4\right)+30\left(4-x\right)-10x+15\left(x-2\right)=0\)
\(\Leftrightarrow6x+24+120-30x-10x+15x-30=0\)
\(\Leftrightarrow-19x+114=0\)
\(\Leftrightarrow-19x=-114\)
hay x=6
Vậy: x=6
d) Ta có: \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\)
\(\Leftrightarrow\frac{21\left(4x+3\right)}{105}-\frac{15\left(6x-2\right)}{105}-\frac{35\left(5x+4\right)}{105}-\frac{315}{105}=0\)
\(\Leftrightarrow84x+63-90x+30-175x-140-315=0\)
\(\Leftrightarrow-181x-362=0\)
\(\Leftrightarrow-181x=362\)
hay x=-2
Vậy: x=-2
e) Ta có: \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right)-\frac{1}{3}\left(x+2\right)\)
\(\Leftrightarrow\frac{x+3}{4}=3-\frac{x+1}{2}-\frac{x+2}{3}\)
\(\Leftrightarrow\frac{3\left(x+3\right)}{12}-\frac{36}{12}+\frac{6\left(x+1\right)}{12}+\frac{4\left(x+2\right)}{12}=0\)
\(\Leftrightarrow3x+9-36+6x+6+4x+8=0\)
\(\Leftrightarrow13x-13=0\)
\(\Leftrightarrow13x=13\)
hay x=1
Vậy: x=1
NB
17 tháng 9 2019
a)\(\left(x-2,5\right)^2=\frac{4}{9}\\ \left(x-\frac{5}{2}\right)^2=\left(\pm\frac{2}{3}\right)^2\\\Leftrightarrow\left\{{}\begin{matrix}x-\frac{5}{2}=\frac{2}{3}\\x-\frac{5}{2}=\frac{-2}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{19}{6}\\x=\frac{11}{6}\end{matrix}\right. \)
vậy....
b)\(\left(2x+\frac{1}{3}\right)^3=\frac{-8}{27}\\ \left(2x+\frac{1}{3}\right)^3=\left(\frac{-2}{3}\right)^3\\ 2x+\frac{1}{3}=\frac{-2}{3}\\ x=\frac{-1}{2}\)
vậy...
15 tháng 6 2020
a, Câu hỏi của Nguyễn Ánh Ngân - Toán lớp 6 - Học toán với OnlineMath
b, Câu hỏi của Vũ Xuân Hiếu - Toán lớp 6 | Học trực tuyến
c)
a) x3 - 125 = x3 - 53 = ( x - 5 )( x2 + 5x + 25 )
b) a3 + 27 = a3 + 33 = ( a + 3 )( a2 - 3a + 9 )
c) -64 + 1/8x3 = ( 1/2x )3 - 43 = ( 1/2x - 4 )( 1/4x2 + 2x + 16 )
d) 0, 001 - 1000x3 = ( 1/10 )3 - ( 10x )3 = ( 1/10 - 10x )( 1/100 + x + 100x2 )
e) ( x + 1 )3 - ( 2 - x )3 = [ ( x + 1 ) - ( 2 - x ) ][ ( x + 1 )2 + ( x + 1 )( 2 - x ) + ( 2 - x )2 ]
= ( x + 1 - 2 + x )( x2 + 2x + 1 - x2 + x + 2 + 4 - 4x + x2 )
= ( 2x - 1 )( x2 - x + 7 )
f) 1/125 + ( x - 1/5 )3 = ( 1/5 )3 + ( x - 1/5 )3
= [ 1/5 + ( x - 1/5 ) ][ 1/25 - 1/5( x - 1/5 ) + ( x - 1/5 )2 ]
= ( 1/5 + x - 1/5 )( 1/25 - 1/5x + 1/25 + x2 - 2/5x + 1/25 )
= x( x2 - 3/5x + 3/25 )
Bài làm :
\(a)x^3-125=x^3-5^3=\left(x-5\right)\left(x^2+5x+25\right)\)
\(b)a^3+27=a^3+3^3=\left(a+3\right)\left(a^2-3a+9\right)\)