- #1
martinrandau
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I have a problem of where to start on this equation.
sqrt(x^2-x-10) = 10 + sqrt(x^2 - 11x)
Solve for x.
sqrt(x^2-x-10) = 10 + sqrt(x^2 - 11x)
Solve for x.
Solving for x: sqrt(x^2-x-10) = 10 + sqrt(x^2-11x)
- Thread starter martinrandau
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In summary, to solve the given equation, you need to square both sides, isolate the square root on one side, and then square both sides again to eliminate the square roots. However, this may introduce false solutions, so it's important to check each expression under a square root to ensure they are not negative. The final solution is x = 11.
- #2
TD
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Square both sides, you'll get another square root on the RHS, isolate it on one side and square both sides again. Then you lost all square roots and you'll be able to solve.
Note: by squaring you may introduce new solutions. You'll have to check those, each expression under a root can't be negative, so cancel out false solutions.
Note: by squaring you may introduce new solutions. You'll have to check those, each expression under a root can't be negative, so cancel out false solutions.
- #3
bomba923
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Just expanding on what TD said,
[tex] \sqrt {x^2 - x - 10} = 10 + \sqrt {x^2 - 11x} \Rightarrow x^2 - x - 10 = 100 + 20\sqrt {x^2 - 11x} + x^2 - 11x \Rightarrow [/tex]
[tex] x - 11 = 2\sqrt {x^2 - 11x} \Rightarrow 3x^2 - 22x - 121 = 0 \Rightarrow x = \frac{{22 \pm \sqrt {22^2 + 1452} }}{6} \Rightarrow x = \left\{ { - \frac{{11}}{3},11} \right\} [/tex]
However, you probably want *[tex] \boxed{x = 11} [/tex]* because [itex] -11 / 3 [/itex] won't work!
Why? Because squaring [itex] x - 11 = 2\sqrt {x^2 - 11x} [/itex] introduces false solutions!
[tex] \sqrt {x^2 - x - 10} = 10 + \sqrt {x^2 - 11x} \Rightarrow x^2 - x - 10 = 100 + 20\sqrt {x^2 - 11x} + x^2 - 11x \Rightarrow [/tex]
[tex] x - 11 = 2\sqrt {x^2 - 11x} \Rightarrow 3x^2 - 22x - 121 = 0 \Rightarrow x = \frac{{22 \pm \sqrt {22^2 + 1452} }}{6} \Rightarrow x = \left\{ { - \frac{{11}}{3},11} \right\} [/tex]
However, you probably want *[tex] \boxed{x = 11} [/tex]* because [itex] -11 / 3 [/itex] won't work!
Why? Because squaring [itex] x - 11 = 2\sqrt {x^2 - 11x} [/itex] introduces false solutions!
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1. What is the brainstorming process for generating ideas/solutions?
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To ensure practicality and feasibility, it can be helpful to conduct research and gather data, consider the limitations and resources available, and seek feedback and input from others. Prototyping and testing can also help determine the viability of an idea or solution.
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