Solve Radical Equations
Solve the radical equation, and check all proposed solutions.
-$y = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1$
A) $3 , - 1$
B) 3
C) $- 3 , - 1$
D) No $x$-intercepts

Question

Quizplus · Accepted Answer

Squaring both sides of the equation and simplifying gives $2x + 3 - 2\sqrt{(2x + 3)(x + 1)} + x + 1 - 2\sqrt{x + 1} + 1 = 0$. Squaring again and simplifying gives $9x^2 + 30x + 25 = 0$. Factoring and solving gives $x = -1$ or $x = -5/3$. Checking shows that $x = -1$ is a solution, but $x = -5/3$ is not.

Solve Radical Equations Solve the Radical Equation, and Check All y=2x+3−x+1−1y = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1y=2x+3​−x+1​−1

Solve Radical Equations
Solve the Radical Equation, and Check All $y = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1$