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How to use it?
- Inequation:
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4^(x-0,5)+1/9*4^x-16^x+0,5-2<=0,5
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((2-x^2)*(x-3)^3)/((x+1)*(x^2-3x-4))>=0
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Identical expressions
- four ^(x- zero , five)+ one / nine * four ^x- sixteen ^x+ zero , five - two <= zero , five
- 4 to the power of (x minus 0,5) plus 1 divide by 9 multiply by 4 to the power of x minus 16 to the power of x plus 0,5 minus 2 less than or equal to 0,5
- four to the power of (x minus zero , five) plus one divide by nine multiply by four to the power of x minus sixteen to the power of x plus zero , five minus two less than or equal to zero , five
- 4(x-0,5)+1/9*4x-16x+0,5-2<=0,5
- 4x-0,5+1/9*4x-16x+0,5-2<=0,5
- 4^(x-0,5)+1/94^x-16^x+0,5-2<=0,5
- 4(x-0,5)+1/94x-16x+0,5-2<=0,5
- 4x-0,5+1/94x-16x+0,5-2<=0,5
- 4^x-0,5+1/94^x-16^x+0,5-2<=0,5
- 4^(x-0,5)+1/9*4^x-16^x+0,5-2<=O,5
- 4^(x-0,5)+1 divide by 9*4^x-16^x+0,5-2<=0,5
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Similar expressions
- 4^(x+0,5)+1/9*4^x-16^x+0,5-2<=0,5
- 4^(x-0,5)+1/9*4^x-16^x+0,5+2<=0,5
- 4^(x-0,5)-1/9*4^x-16^x+0,5-2<=0,5
- 4^(x-0,5)+1/9*4^x-16^x-0,5-2<=0,5
- 4^(x-0,5)+1/9*4^x+16^x+0,5-2<=0,5
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What you mean?
- -16^x + (2688086027586765/140737488355328)^(4^x) + 4^(x - 1*13/2) - 1*2 + 13/2 <= 1/2
4^(x-0,5)+1/9*4^x-16^x+0,5-2<=0,5 inequation
The solution
You have entered
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x
x - 1/2 4 x 1
4 + -- - 16 + - - 2 <= 1/2
9 2
$$- 16^{x} + \frac{4^{x}}{9} + 4^{x - \frac{1}{2}} - 2 + \frac{1}{2} \leq \frac{1}{2}$$
-16^x + 4^x/9 + 4^(x - 1*1/2) - 1*2 + 1/2 <= 1/2
Detail solution
Given the inequality:
$$- 16^{x} + \frac{4^{x}}{9} + 4^{x - \frac{1}{2}} - 2 + \frac{1}{2} \leq \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$- 16^{x} + \frac{4^{x}}{9} + 4^{x - \frac{1}{2}} - 2 + \frac{1}{2} = \frac{1}{2}$$
Solve:
$$x_{1} = \frac{\log{\left(- \sqrt[4]{2} e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2}} \right)}}{\log{\left(2 \right)}}$$
$$x_{2} = \frac{1}{4} + \frac{\log{\left(- e^{\frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2}} \right)}}{\log{\left(2 \right)}}$$
$$x_{3} = \frac{1}{4} - \frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2 \log{\left(2 \right)}}$$
$$x_{4} = \frac{1}{4} + \frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2 \log{\left(2 \right)}}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$x_0 = 0$$
$$\left(-1\right) 2 - 16^{0} + \frac{4^{0}}{9} + 4^{\left(-1\right) \frac{1}{2} + 0} + \frac{1}{2} \leq \frac{1}{2}$$
so the inequality is always executed
$$- 16^{x} + \frac{4^{x}}{9} + 4^{x - \frac{1}{2}} - 2 + \frac{1}{2} \leq \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$- 16^{x} + \frac{4^{x}}{9} + 4^{x - \frac{1}{2}} - 2 + \frac{1}{2} = \frac{1}{2}$$
Solve:
$$x_{1} = \frac{\log{\left(- \sqrt[4]{2} e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2}} \right)}}{\log{\left(2 \right)}}$$
$$x_{2} = \frac{1}{4} + \frac{\log{\left(- e^{\frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2}} \right)}}{\log{\left(2 \right)}}$$
$$x_{3} = \frac{1}{4} - \frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2 \log{\left(2 \right)}}$$
$$x_{4} = \frac{1}{4} + \frac{i \operatorname{atan}{\left(\frac{\sqrt{2471}}{11} \right)}}{2 \log{\left(2 \right)}}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$x_0 = 0$$
$$\left(-1\right) 2 - 16^{0} + \frac{4^{0}}{9} + 4^{\left(-1\right) \frac{1}{2} + 0} + \frac{1}{2} \leq \frac{1}{2}$$
-17/9 <= 1/2
so the inequality is always executed
Solving inequality on a graph
The graph