Question

What are the solution(s) to the quadratic equation 9x2 = 4? x = StartFraction 4 Over 9 EndFraction and x = StartFraction negative 4 Over 9 EndFraction x = StartFraction 2 Over 3 EndFraction and x = StartFraction negative 2 Over 3 EndFraction x = StartFraction 3 Over 2 EndFraction and x = StartFraction negative 3 Over 2 EndFraction no real solution

Answer 1

Answer:

$S=\left \{x \in\mathbb{R}| x= \pm \frac{2}{3} \right \}$

Or

x = StartFraction negative 2 Over 3 EndFraction.

Step-by-step explanation:

As in this quadratic equation, b and c parameters are equal to zero. We can simply divide everything by 9 and then take the square root of all members of this equation. This equation has two solutions since Δ > 0, so we can write the solution formally as  $S=\left \{x \in\mathbb{R}| x= \pm \frac{2}{3} \right \}$

$9x^{2}=4\\\frac{9x^{2}}{9}=\frac{4}{9}\Rightarrow x^{2}=\frac{4}{9}\Rightarrow \sqrt{x^{2}}=\sqrt{\frac{4}{9}}\\x=\pm \frac{2}{3}\Rightarrow S=\left \{x \in\mathbb{R}| x= \pm \frac{2}{3} \right \}$

Answer 2

Answer:

x = StartFraction 2 Over 3 EndFraction and x = StartFraction negative 2 Over 3 EndFraction.

Step-by-step explanation:

We are given a quadratic equation of single variable x as $9x^{2} =4$.

There is no doubt that as the equation is of two degrees so, it will have two solutions.

Now, $9x^{2} =4$

⇒ $x^{2} =\frac{4}{9}$

⇒ $x=\frac{2}{3}$  and $x = -\frac{2}{3}$

Therefore, the solution will be x = StartFraction 2 Over 3 EndFraction and x = StartFraction negative 2 Over 3 EndFraction. (Answer)