Solve Radical Equations
-$$x - \sqrt { 3 x - 2 } = 4$$
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 yields $(x - 9)(x - 2) = 0$, so $x = 9$ or $x = 2$. However, when $x = 2$ is substituted back into the original equation, it does not satisfy the equation, leaving $x = 9$ as the only solution.

Solve Radical Equations - x−3x−2=4x - \sqrt { 3 x - 2 } = 4x−3x−2​=4

Solve Radical Equations
- $x - \sqrt { 3 x - 2 } = 4$