Solve the equation.
-$$( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$$

Question

Quizplus · Accepted Answer

To solve the equation $(3x + 1)^{1/2} = 3 + (x - 4)^{1/2}$, we first square both sides to eliminate the square roots, leading to $3x + 1 = 9 + 6(x - 4)^{1/2} + x - 4$. Simplifying and rearranging gives a quadratic equation in terms of $(x - 4)^{1/2}$, which can be solved to find the values of $x$. The correct solutions that satisfy the original equation are $x = 5$ and $x = 8$, making choice B the correct answer.

Solve the Equation (3x+1)1/2=3+(x−4)1/2( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }(3x+1)1/2=3+(x−4)1/2

Solve the Equation $( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$