$$\sqrt{\frac{x}2} = 1-x$$ so $$x = ?$$ I have tried to solve many times and i got $x = \frac52$ everytime. But my book says answer is $\frac12$. I think i couldn't understand square roots clearly.. So, Where is my mistake ? Give me a hint or show how to solve it.

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    $\begingroup$ "Where is my mistake?" Show us your work!! $\endgroup$ – Alex Silva Apr 9 '15 at 10:43

$$\sqrt{\frac{x}2} = 1-x\implies \frac{x}{2}=(1-x)^2=1+x^2-2x\\ \implies x=2+2x^2-4x\\ \implies 2x^2-5x+2=0\\ \implies (2x-1)(x-2)=0\\ \implies x\in\left\{\frac{1}{2},2\right\}$$

But $x=2$ makes the original equation $1=(-1)$ which is false.

Hence, we have the only solution $x=\dfrac{1}{2}$

  • $\begingroup$ Thank you very much. I had missed coefficient of $x^2$ in my operations.. $\endgroup$ – Oğuz İsmayil uysal Apr 9 '15 at 10:43
  • $\begingroup$ @Oğuzİsmayiluysal, you're welcome. :) If it helped you, you can "accept" it by clicking on the check mark on my answer. :) $\endgroup$ – Prasun Biswas Apr 9 '15 at 10:45

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