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\(x\left(x-1\right)=157\)
=>\(x^2-x-157=0\)
\(\Delta=\left(-1\right)^2-4\cdot1\cdot\left(-157\right)=629>0\)
Do đó: Phương trình có hai nghiệm phân biệt là:
\(\left[\begin{array}{l}x=\frac{1-\sqrt{629}}{2\cdot1}=\frac{1-\sqrt{629}}{2}\\ x=\frac{1+\sqrt{629}}{2\cdot1}=\frac{1+\sqrt{629}}{2}\end{array}\right.\)
bài này là cô lớp sáu giao cho em ý em còn chưa học cái đó nữa
Ta có: A = 3 + 32 + 33 + ... + 3100
=> 3A = 32 + 33 + 34 + ... + 3101
=> 3A - A = 3101 - 3
=> 2A = 3101 - 3
=> 2A + 3 = 3101
=> x = 101
\(2A=3^2+3^3+...+3^{101}\)
\(2A-A=3^2-3^2+3^3-3^3+...+3^{101}-3\)
\(A=3^{101}-3\)
\(2.3^{101}-6+3=3^x\)
\(3.\left(2.3^{100}-1\right)=3^x\)
\(\left(3\dfrac{1}{2}-x\right).1\dfrac{1}{4}=-1\dfrac{1}{20}\)
\(\left(\dfrac{7}{2}-x\right).\dfrac{5}{4}=-\dfrac{21}{20}\)
\(\dfrac{7}{2}-x=-\dfrac{21}{20}:\dfrac{5}{4}\)
\(\dfrac{7}{2}-x=-\dfrac{21}{25}\)
\(x=\dfrac{7}{2}-\left(-\dfrac{21}{25}\right)\)
\(x=\dfrac{217}{50}\)
Vậy \(x=\dfrac{217}{50}\)\(\)
\(\frac{b}{a}\).(\(\frac{1}{n}\) - \(\frac{1}{n+a}\))
= \(\frac{b}{a}\).\(\frac{n+a-n}{n\left(n+a\right)}\)
= \(\frac{b}{a}.\) \(\frac{\left(n-n\right)+a}{n\left(n+a\right)}\)
= \(\frac{b}{a}\).\(\frac{a}{n\left(n+a\right)}\)
= \(\frac{b}{n\left(n+a\right)}\) (đpcm)
\(\frac{x}{3}=\frac{2}{3}-\frac{1}{7}\)
\(\Leftrightarrow\frac{x}{3}=\frac{11}{21}\)
\(\Leftrightarrow21x=33\)
\(\Leftrightarrow x=\frac{33}{21}=\frac{11}{7}\)
b1:
\(-5.\left(x-\frac{1}{5}\right)-\frac{1}{2}\left(x-\frac{2}{3}\right)=\frac{3}{2}x-\frac{5}{6}\Leftrightarrow-5x+1-\frac{1}{2}x+\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)
\(\Leftrightarrow-\frac{11}{2}x+\frac{4}{3}=\frac{3}{2}x-\frac{5}{6}\Leftrightarrow-\frac{11}{2}x-\frac{3}{2}x=-\frac{5}{6}-\frac{4}{3}\Leftrightarrow-7x=-\frac{13}{6}\)
\(\Leftrightarrow x=\frac{-13}{6}:\left(-7\right)=\frac{13}{42}\)
b2:
a)\(3^{3x-1}=9^{x-2}\Leftrightarrow3^{3x-1}=\left(3^2\right)^{x-2}\Leftrightarrow3^{3x-1}=3^{2x-4}\Leftrightarrow3x-1=2x-4\)
<=>3x-2x=-4+1<=>x=-3
b)\(\left(x-1\right)^4=\left(x-1\right)^6\Leftrightarrow\left(x-1\right)^4-\left(x-1\right)^6=0\Leftrightarrow\left(x-1\right)^4\left[1-\left(x-1\right)^2\right]=0\)
\(\Leftrightarrow\left(x-1\right)^4\left[1-\left(x^2-2x+1\right)\right]=0\Leftrightarrow\left(x-1\right)^4\left(1-x^2+2x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)^4\left(-x^2+2x\right)=0\Leftrightarrow\left(x-1\right)^4.\left(-x\right).\left(x-2\right)=0\)
<=>(x-1)4=0 hoặc -x=0 hoặc x-2=0 <=> x=1 hoặc x=0 hoặc x=2
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
A,\(\frac{2}{3}+\frac{1}{2}:3x=20\%\)
B,\(\frac{1}{2}.x-\frac{2}{3}.x=\frac{7}{12}\)
Giúp tui vs!!!!!!
2/3 + 1/2:3x=20/100
1/2:3x=20/100-2/3=-7/15
3x=1/2:-7/15
x=-15/14:3=-5/14
x[1/2-2/3]=7/12
x. -1/6=7/12
x=7/12:-1/6=-3,5
15-(x+2)=20
x+2=15-20
x+2=-5
x=-5-2
x=-7
vậy x=-7