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Kenneth Rosen Edition 7 Exercise 1.7 Question 35 (Page No. 91)

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Are these steps for finding the solutions of $\sqrt{x+3=3−x}$ correct?

  1. $\sqrt{x+3=3−x}$ is given;
  2. $x+3=x2−6x+9$, obtained by squaring both sides of(1);
  3. $0=x2−7x+6$, obtained by subtracting $x+3$ from both sides of(2);
  4. $0=(x−1)(x−6)$, obtained by factoring the right-hand side of(3);
  5. $x=1$ or $x=6$,which follows from(4) because $ab=0$ implies that $a=0$ or $b=0$.
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