Solve Radical Equations
Solve the radical equation, and check all proposed solutions.
-$$x - \sqrt { 3 x - 2 } = 4$$
A) $\{ 9 \}$
B) $\{ 2,9 \}$
C) $\{ - 1 \}$
D) $\{ 1,2 \}$

Question

Quizplus · Accepted Answer

To solve the equation $x - \sqrt{3x - 2} = 4$, first isolate the square root term: $\sqrt{3x - 2} = x - 4$. Then square both sides to eliminate the square root: $(x - 4)^2 = 3x - 2$. Expanding and simplifying gives $x^2 - 8x + 16 = 3x - 2$, which simplifies to $x^2 - 11x + 18 = 0$. Factoring this quadratic equation gives $(x - 9)(x - 2) = 0$, so the potential solutions are $x = 9$ and $x = 2$. Checking these in the original equation, only $x = 9$ satisfies the equation, making it the correct solution.

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

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