Solve Radical Equations
When you learned about systems of equations, one of the methods for solving that you learned about was to solve by graphing. We're going to solve radical equations by graphing in this investigation. You may use the graphing calculator here to graph and find the solution.
When you learned about systems of equations, one of the methods for solving that you learned about was to solve by graphing. We're going to solve radical equations by graphing in this investigation. You may use the graphing calculator here to graph and find the solution.
Solve the system of equations.
1) \(y=\sqrt[3]{x+3}\) \(y=2\) How many solutions are there to this system? 2) \(y=\sqrt{x-4}+3\) \(y=\sqrt{2x+6}\) How many solutions are there to this system? 3) \(y=\frac{1}{2}\sqrt{5x-1}\) \(y=\sqrt{3}\) How many solutions are there to this system? 4) \(y=\frac{1}{2}\sqrt[3]{x^2+5x+4}+3\) \(y=3\) How many solutions are there to this system? |
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Sometimes when you want to solve an equation, an effective way to solve is by turning the equation into a system and solving by graphing. For example to solve \(x^2+2x+8=8\) you could graph \(y=x^2+2x+8\) and \(y=8\). You'll notice that the solutions are \(x=-2\) and \(x=0\).
Notice that when you solve one equation, you are looking for a solution for the unknown variable, you are NOT looking for an ordered pair. This is because the equation only has one variable, usually \(x\). You are not looking for \((x, y)\) because the \(y\) never existed in the original equation.
Solve the equation.
1) \(\frac{3}{4}\sqrt{3x+8}=\sqrt{x+10}\) How many solutions are there to this equation? 2) \(\sqrt{x-4}+\sqrt{2x-1}=4\) How many solutions are there to this equation? 3) \(\left(x^2+2\right)^{\frac{2}{3}}+1=10\) How many solutions are there to this equation? |
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