Tìm x:
-3x+(-5/12)=8
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a: =>(3x+1)(3x-1)-(3x+1)(2x-3)=0
=>(3x+1)(3x-1-2x+3)=0
=>(3x+1)(x+2)=0
=>x=-1/3 hoặc x=-2
b: =>(3x+1)(6x+2)-(3x+1)(x-2)=0
=>(3x+1)(6x+2-x+2)=0
=>(3x+1)(5x+4)=0
=>x=-1/3 hoặc x=-4/5
1.
\(\dfrac{1-cosx+cos2x}{sin2x-sinx}=\dfrac{1-cosx+2cos^2x-1}{2sinx.cosx-sinx}\)
\(=\dfrac{cosx\left(2cosx-1\right)}{sinx\left(2cosx-1\right)}=\dfrac{cosx}{sinx}=cotx\)
2.
\(\dfrac{1+tan^4x}{tan^2x+cot^2x}=\dfrac{1+tan^4x}{tan^2x+\dfrac{1}{tan^2x}}=\dfrac{1+tan^4x}{\dfrac{tan^4x+1}{tan^2x}}=tan^2x\)
3.
\(sin^4x+cos^4x=sin^4x+cos^4x+2sin^2x.cos^2x-2sin^2x.cos^2x\)
\(=\left(sin^2x+cos^2x\right)^2-2sin^2x.cos^2x\)
\(=1-2sin^2x.cos^2x\)
4.
Áp dụng câu 3:
\(sin^4x+cos^4x=1-2sin^2x.cos^2x\)
\(=1-\dfrac{1}{2}\left(2sinx.cosx\right)^2\)
\(=1-\dfrac{1}{2}sin^22x\)
5.
\(sin\left(x+y\right)sin\left(x-y\right)=\dfrac{1}{2}cos\left[\left(x-y\right)-\left(x+y\right)\right]-\dfrac{1}{2}cos\left[\left(x-y\right)+\left(x+y\right)\right]\)
\(=\dfrac{1}{2}\left(cos2y-cos2x\right)=\dfrac{1}{2}\left(1-2sin^2y\right)-\dfrac{1}{2}\left(1-2sin^2x\right)\)
\(=sin^2x-sin^2y\)
6.
\(tanx+cotx=\dfrac{sinx}{cosx}+\dfrac{cosx}{sinx}=\dfrac{sin^2x+cos^2x}{sinx.cosx}\)
\(=\dfrac{1}{sinx.cosx}=\dfrac{2}{2sinx.cosx}=\dfrac{2}{sin2x}\)
Ta có: \(\frac{x+2}{y+10}\)\(=\)\(\frac{1}{5}\)\(\Rightarrow\)\(5\left(x+2\right)=y+10\)(1)
\(y-3x=2\)\(\Rightarrow\)\(y+2=3x\) (2)
Thay (2) vào (1) ta có:
\(5\left(x+2\right)=\left(y+2\right)+8\)
\(5x+10=3x+8\)
\(5x-3x=8-10\)
\(2x=-2\)
\(x=-2:2\)
\(x=-1\)
Vậy: x=-1
Chúc bạn làm bài tốt!
a,
(x2-x+1)(x+1)-x3+3x=15
x3-x2+x+x2-x+1-x3+3x=15
x3-x3-x2+x2+x-x+3x+1=15
3x+1=15
3x=15-1
3x=14
x=14/3
b,
(x+3)(x-2)+3x=\(\frac{4}{x+\frac{3}{4}}\)
x2-2x+3x-6+3x=\(\frac{4}{x+\frac{3}{4}}\)
x2-2x+3x+3x-6=\(\frac{4}{x+\frac{3}{4}}\)
Tới đây hết biết , đề có gì sai sai sao ý !
c,
(x2-5)(x+2)+5x=2x2+17
x3+2x2-5x-10+5x=2x2+17
x3+2x2-5x+5x-10=2x2+17
x3+2x2-10=2x2+17
x3-10=17
x3=17+10
x3=27
\(\Rightarrow x=3\)(Vì : 33=27)
_k_ nhé bn
Nhân ra thôi bạn, có hằng đẳng thức gì đâu !
a) \(\left(x^2-x+1\right)\left(x+1\right)-x^3+3x=15\)
\(\Leftrightarrow\left(x^2-x+1\right)\cdot x+x^2-x+1-x^3+3x=15\)
\(\Leftrightarrow x^3-x^2+x+x^2-x+1-x^3+3x=15\)
\(\Leftrightarrow1+3x=15\Leftrightarrow3x=14\Leftrightarrow x=\frac{14}{3}\)
b) \(\left(x+3\right)\left(x-2\right)+3x=4\cdot\left(x+\frac{3}{4}\right)\)
\(\Leftrightarrow x^2+3x-2x-6+3x=4x+3\)
\(\Leftrightarrow x^2+4x-6=4x+3\)
\(\Leftrightarrow x^2=9\Leftrightarrow\orbr{\begin{cases}x=-3\\x=3\end{cases}}\)
c) \(\left(x^2-5\right)\left(x+2\right)+5x=2x^2+17\)
\(\Leftrightarrow x^3-5x+2x^2-10+5x=2x^2+17\)
\(\Leftrightarrow x^3=27\Leftrightarrow x=3\)
\(-3x+\left(-\dfrac{5}{12}\right)=8\)
\(\Rightarrow-3x-\dfrac{5}{12}=8\)
\(\Rightarrow-3x=8+\dfrac{5}{12}\)
\(\Rightarrow-3x=\dfrac{101}{12}\)
\(\Rightarrow x=\dfrac{101}{12}\div\left(-3\right)\)
\(\Rightarrow x=-\dfrac{101}{36}\)
`-3x+(-5/12)=8`
`-3x-5/12=8`
`-3x=8+5/12`
`-3x =101/12`
`x=-101/12:3`
`x=-101/12 xx 1/3`
`x=-101/36`
Vậy `x=-101/36`