Find the x-intercepts of the graph of the equation.
-$$y = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1$$
A) $3 , - 1$
B) 3
C) $- 3 , - 1$
D) No x-intercepts

Question

Quizplus · Accepted Answer

To find the x-intercepts, set y = 0 and solve for x.$0 = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1$$\sqrt { 2 x + 3 } = \sqrt { x + 1 } + 1$Squaring both sides:$2 x + 3 = x + 1 + 2 \sqrt { x + 1 } + 1$$x + 2 = 2 \sqrt { x + 1 }$Squaring both sides again:$(x + 2)^2 = (2 \sqrt { x + 1 })^2$$x^2 + 4 x + 4 = 4(x + 1)$$x^2 + 4 x + 4 = 4x + 4$$x^2 = 0$$x = 0$Therefore, the x-intercept is (0, 0).

Find the X-Intercepts of the Graph of the Equation y=2x+3−x+1−1y = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1y=2x+3​−x+1​−1

Find the X-Intercepts of the Graph of the Equation $y = \sqrt { 2 x + 3 } - \sqrt { x + 1 } - 1$