Question

question 3 of 10 which of the following are solutions to the equation below? check all that apply. (3x - 5)^2 = 19 a x = -√19 + 5/3 b x = √19/3 c x = -√19/3 d x = √19 + 5/3 e x = (√19 + 5)/3 f x = (-√19 + 5)/3

Explanation:

Step1: Take square - root of both sides

If \((3x - 5)^2=19\), then \(3x-5=\pm\sqrt{19}\).

Step2: Solve for \(x\) when \(3x - 5=\sqrt{19}\)

Add 5 to both sides: \(3x=\sqrt{19}+5\). Then divide by 3: \(x = \frac{\sqrt{19}+5}{3}\).

Step3: Solve for \(x\) when \(3x - 5=-\sqrt{19}\)

Add 5 to both sides: \(3x=-\sqrt{19}+5\). Then divide by 3: \(x=\frac{-\sqrt{19}+5}{3}\).

Answer:

A. \(x =-\sqrt{19}+\frac{5}{3}\), E. \(x=\frac{\sqrt{19}+5}{3}\), F. \(x=\frac{-\sqrt{19}+5}{3}\)