\(^{x^3+9.x^2+27.x+27}\)
giải các bất phương trình
a) \(27^{2-x}\le9\)
b) \(7^{3-x}< 49\)
c) \(27^{3-x}>9\)
d) \(2^{3-x}< 2^3\)
e) \(27^{3-x^2}< 27^{x+1}\)
a: \(27^{2-x}< =9\)
=>\(\left(3^3\right)^{2-x}< =3^2\)
=>\(3^{6-3x}< =3^2\)
=>6-3x<=2
=>-3x<=-4
=>\(x>=\dfrac{4}{3}\)
b: \(7^{3-x}< 49\)
=>\(7^{3-x}< 7^2\)
=>3-x<2
=>-x<2-3=-1
=>x>1
c: \(27^{3-x}>9\)
=>\(\left(3^3\right)^{3-x}>3^2\)
=>\(3^{9-3x}>3^2\)
=>9-3x>2
=>-3x>-7
=>\(x< \dfrac{7}{3}\)
d: \(2^{3-x}< 2^3\)
=>3-x<3
=>-x<0
=>x>0
e: \(27^{3-x^2}< 27^{x+1}\)
=>\(3-x^2< x+1\)
=>\(-x^2-x+2< 0\)
=>\(x^2+x-2>0\)
=>(x+2)(x-1)>0
=>\(\left[{}\begin{matrix}x>1\\x< -2\end{matrix}\right.\)
Tính:
a) 2^5 x 13^12 x 7^8 : 27 x 13^10 x 7^9
b) 2^n x 11 x 3 : 6^n x 3
c) 5^5 x 7 x 9^5 : 15^10
d) 7 x 8^10 x 27^9 - 8 x 9^13 x 2^27 : 7 x 6^26 x 2^2 - 2^4 x 8^3 x 27^9
e) 2^2^1^2015
f) 2015^0^2015^0^2015
x^3+27=27=9-x^2
x^3+27=27
x=0
=>27=9-0^2
=>27=9
=>x không tồn tại
1/3(1-4x)(x-1) +4(3x-2) (x+3)=-27
2/ (x+3) (x^2 -3x+9)-x(x-1)(x+1)=27
1/
\(3\left(-1-4x^2+5x\right)+4\left(3x^2+7x-6\right)=-27\)
\(\Leftrightarrow-3-12x^2+15x+12x^2+28x-24=-27\)
\(\Leftrightarrow43x=0\Rightarrow x=0\)
2/
\(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x^2-1\right)=27\)
\(\Leftrightarrow x^3+27-x^3+x=27\)
\(\Leftrightarrow x=0\)
câu 3
ta có \(\frac{x}{-3}\)=y/5 => x=\(\frac{-3y}{5}\)
thay x= -3y/5 vào xy=-5/27 ta được
-\(\frac{-3y}{5}\)*y=-5/27
=>\(\frac{-3y^{^2}}{5}\)=-5/27
=>.-3y^2 =-5/27 :5=-5/27*1/5
=> -3y^2=-1/27
=>y^2 =-1/27 :(-3)=-1/27*(-1/3)=1/81
=>y=1/9
Khi đó x= -5/27 : 1/9 = -5/27 *9 = -5/3
vậy x= -5/3 ,y = 1/9
Tính nhanh:
2/3 x 4/5 + 4/5 x 8/3 27/32 x 16/9 - 27/32 x 7/9 + 27/32
2/3 x 4/5 + 4/5 x 8/3 = 4/5 x (2/3 + 8/3) = 4/5 x 10/3 = 8/3
27/32 x 16/9 -27/32 x7/9 + 27/32
= 27/32 x (16/9 - 7/9 + 1 )
=27/32 x 2
=27/16
\(\frac{2}{3}\) x \(\frac{4}{5}\) + \(\frac{4}{5}\) x \(\frac{8}{3}\)
=\(\frac{4}{5}\) x ( \(\frac{2}{3}\) + \(\frac{8}{3}\) )
= \(\frac{4}{5}\) x \(\frac{10}{3}\)
= \(\frac{40}{15}\) = \(\frac{8}{5}\)
giải phương trình 27*x^3 +18*x^2-9*x+(27*x^2+2*x-1)cawn2x-1 -125=0
\(\frac{2}{x-3}-\frac{27}{x^3-27}=\frac{3}{x^2+3x+9}\)
\(\frac{2}{x-3}\)-\(\frac{27}{x^3-27}\)=\(\frac{3}{x^2+3x+9}\)
\(\frac{2}{x-3}\)-\(\frac{27}{\left(x-3\right)\left(x^2+3x+9\right)}\)=\(\frac{3}{x^2+3x+9}\)
\(\frac{2\left(x^2+3x+9\right)}{\left(x-3\right)\left(x^2+3x+9\right)}\)-\(\frac{27}{\left(x-3\right)\left(x^2+3x+9\right)}\)=\(\frac{3\left(x-3\right)}{\left(x-3\right)\left(x^2+3x+9\right)}\)
2x2+6x+18-27=3x-9 2x2+6x-3x=27-18-9 2x2+3x=0 x(2x+3)=0 x=0 hoặc 2x+3=0 x=0 hoặc x=\(\frac{-3}{2}\)tìm x
3x /27=27
9x-1 =1/9
32/2x=4
27/3x=3
9x:3x=32015
2 x 3x + 3x-1=7-(32+ 2 x 62)
7x+2 + 2 x 7x-1=345
j mà j mà hjhj thế nguyenthuy thế trieu dang
\(\frac{3^x}{27}=27\Rightarrow\frac{3^x}{27}=\frac{729}{27}=\frac{3^6}{27}\)
\(\Rightarrow3^x=3^6\Rightarrow x=6\)