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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

Respuesta :

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 [tex]9x^{2} =4[/tex].

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

Now, [tex]9x^{2} =4[/tex]

⇒ [tex]x^{2} =\frac{4}{9}[/tex]

⇒ [tex]x=\frac{2}{3}[/tex]  and [tex]x = -\frac{2}{3}[/tex]

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

profantoniofonte

Answer:

[tex]S=\left \{x \in\mathbb{R}| x= \pm \frac{2}{3} \right \}[/tex]

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  [tex]S=\left \{x \in\mathbb{R}| x= \pm \frac{2}{3} \right \}[/tex]

[tex]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 \}[/tex]

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