Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Got It? - Page 635: 4

No solution

We are given: $-y=\sqrt y+6$ Square each side: $(-y)^2=(\sqrt y+6)^2$ $y^2=y+6$ $y^2-y-6=0$ $(y-3)(y+2)=0$ $y-3=0$ or $y+2=0$ $y=3$ or $y=-2$ Check: $-3=\sqrt -3+6$ or $-2=\sqrt (-2)+6$ $-3 \ne \sqrt 3$ or $-2\ne 2$ Therefore, the original equation has no solution.