algebra

Find all real values of x that satisfy the equation (x^2 - 82)^2 = 25.

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\( \color{BrickRed}(x^2 - 82)^2 = 25\\ x^2=a\\ (a-82)^2-25=0\)

\((a-82+5)(a-82-5)=0\\ a_1-82+5=0\\ a_1=77,\ \ \color{blue}x_{1,2}=\pm \sqrt{77}\\ a_2-82-5=0\\ a_2=87,\ \ \color{blue}x_{3,4}=\pm \sqrt{87}\)

\(x\in\{-\sqrt{87},\ -\sqrt{77},\ +\sqrt{77},\ +\sqrt{87}\}\)

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