Solve Radical Equations
Solve the radical equation, and check all proposed solutions.
-$$\sqrt { 2 \sqrt { x + 3 } } = \sqrt { 4 x - 5 }$$
A) $\left\{ \frac { 11 + \sqrt { 69 } } { 8 } \right\}$
B) $\left\{ \frac { 11 - \sqrt { 69 } } { 8 } , \frac { 11 + \sqrt { 69 } } { 8 } \right\}$
C) $\left\{ \frac { 11 } { 2 } \right\}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

The equation $\sqrt { 2 \sqrt { x + 3 } } = \sqrt { 4 x - 5 }$ simplifies to $2 \sqrt { x + 3 } = 4x - 5$. Solving this quadratic equation gives two solutions, but only $\frac { 11 + \sqrt { 69 } } { 8 }$ satisfies the original equation.

Solve Radical Equations Solve the Radical Equation, and Check All 2x+3=4x−5\sqrt { 2 \sqrt { x + 3 } } = \sqrt { 4 x - 5 }2x+3​​=4x−5​

Solve Radical Equations
Solve the Radical Equation, and Check All $\sqrt { 2 \sqrt { x + 3 } } = \sqrt { 4 x - 5 }$