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a: =>2^4x<2^28

=>4x<28

=>x<7

b: =>5^3x+3<5

=>3x+3<1

=>3x<-2

=>x<-2/3

a) \(16^x< 128^4\)

= (24)^x < (27)⁴

= 2^4x < 2²⁸

= 4x < 28

= x < 7 

Vậy \(x=\left\{0;1;2;3;4;5;6;\right\}\)

\(#Tuyết\)

a) 3x⁴ - 13x³ + 16x² - 13x + 3 = 0

(x - 3)(3x - 1)(x² - x + 1) = 0

nhưng vì x² - x + 1 # 0 nên:

x - 3 = 0 hoặc 3x - 1 = 0

x = 0 + 3         3x = 0 + 1

x = 3               3x = 1

                        x = 1/3

b) 6x⁴ + 5x³ - 38x² + 5x + 6 = 0

(x - 2)(x + 3)(3x + 1)(2x - 1) = 0

x - 2 = 0 hoặc x + 3 = 0 hoặc 3x + 1 = 0 hoặc 2x - 1 = 0

x = 0 + 2         x = 0 - 3           3x = 0 - 1          2x = 0 + 1

x = 2               x = -3               3x = -1              2x = 1

                                                x = -1/3             x = 1/2

a: Ta có: \(x\left(2-x\right)+\left(x^2+x\right)=7\)

\(\Leftrightarrow2x-x^2+x^2+x=7\)

\(\Leftrightarrow3x=7\)

hay \(x=\dfrac{7}{3}\)

b: Ta có: \(\left(2x+1\right)^2-x\left(4-5x\right)=17\)

\(\Leftrightarrow4x^2+4x+1-4x+5x^2=17\)

\(\Leftrightarrow9x^2=16\)

\(\Leftrightarrow x^2=\dfrac{16}{9}\)

hay \(x\in\left\{\dfrac{4}{3};-\dfrac{4}{3}\right\}\)

c: Ta có: \(\left(x-4\right)^2-\left(2x+1\right)^2=0\)

\(\Leftrightarrow\left(x-4-2x-1\right)\left(x-4+2x+1\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=1\end{matrix}\right.\)

d: ta có: \(\dfrac{2x^3-8x^2+10x}{2x}=0\)

\(\Leftrightarrow x^2-4x+5=0\)

\(\Leftrightarrow\left(x-2\right)^2+1=0\)(vô lý)

a, \(16x^2-9\left(x+1\right)^2=0\)

\(\Leftrightarrow\left(4x\right)^2-\left(3x+3\right)^2=0\Leftrightarrow\left(4x-3x-3\right)\left(4x+2x+3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(6x+3\right)=0\Leftrightarrow x=-\frac{1}{2};x=3\)

b, \(\left(5x-4\right)^2-49x^2=0\Leftrightarrow\left(5x-4-7x\right)\left(5x-4+7x\right)=0\)

\(\Leftrightarrow\left(-2x-4\right)\left(12x-4\right)=0\Leftrightarrow x=-2;x=\frac{1}{3}\)

c, \(5x^3-20x=0\Leftrightarrow5x\left(x^2-4\right)=0\)

\(\Leftrightarrow5x\left(x-2\right)\left(x+2\right)=0\Leftrightarrow x=0;x=\pm2\)

1: Ta có: \(16x^2-9\left(x+1\right)^2=0\)

\(\Leftrightarrow\left(4x-3x-3\right)\left(4x+3x+3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(7x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{7}{3}\end{matrix}\right.\)

2: Ta có: \(\left(5x-4\right)^2-49x^2=0\)

\(\Leftrightarrow\left(5x-4-7x\right)\left(5x-4+7x\right)=0\)

\(\Leftrightarrow\left(2x+4\right)\left(12x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{1}{3}\end{matrix}\right.\)

3: Ta có: \(5x^3-20x=0\)

\(\Leftrightarrow5x\left(x-2\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)

x⁴+5x³-x²-16x+10=0

<=>x⁴+3x³-5x²+2x³+6x²-10x-5x²-15x+25=0

<=>x²(x²+3x-5)+2x(x²+3x-5)-5(x²+3x-5)=0

<=>(x²+2x-2)(x²+3x-5)=0

<=>x²+2x-2=0 hoặc x²+3x-5=0

\(\Leftrightarrow x=\pm\sqrt{3}-1\)

\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{\sqrt{29}+3}{2}\\x=\frac{\sqrt{29}-3}{2}\end{cases}}\)

\(-5x^2+16x-3=0\)

\(-5x^2+x+15x-3=0\)

\(x\cdot\left(-5x+1\right)-3\cdot\left(-5x-1\right)=0\)

\(\left(-5x-1\right)\cdot\left(x-3\right)=0\)

\(\hept{\begin{cases}-5x-1=0\\x-3=0\end{cases}\Rightarrow\hept{\begin{cases}x=-\frac{1}{5}\\x=3\end{cases}}}\)

Vậy.......

-5x^2 +15x +x-3=0

5x(-x +3)-(-x+3)= 

(5x-1)(-x+3)=0 

5x-1 =0 hoặc -x+3=0

x=1/5 hoặc x=3

tự ghi lại đề

 -5x^2+15x+x-3=0
 (-5x^2+15x)+(x-3)=0

 -5x(x-3)+(x-3)=0

 (-5x+1)(x-3)=0

 -5x-1=0           -5x=1         x=-1/5 

 x-3=0             x=3           x=3