Question

Solve x=√3x square -2x-8√3 =0

Answer 1

We need to recall the quadratic formula.

The roots of the quadratic equation $ax^{2} +bx+c=0$ are:

  $x=\frac{-b\pm\sqrt{b^2 -4ac} }{2a}$  

Given:

$\sqrt{3}x^{2} -2x-8\sqrt{3}=0$

Here, $a=\sqrt{3}$ , $b=-2$ and $c=-8\sqrt{3}$

Using the quadratic formula, we get

$x=\frac{-(-2)\pm\sqrt{(-2)^2 -4(\sqrt{3})(-8\sqrt{3} )} }{2\sqrt{3} }$

$x=\frac{2\pm\sqrt{4 +32(3)} }{2\sqrt{3} }$

$x=\frac{2\pm\sqrt{4 +96} }{2\sqrt{3} }$

$x=\frac{2\pm\sqrt{100} }{2\sqrt{3} }$

$x=\frac{2\pm10 }{2\sqrt{3} }$

$x=\frac{2(1\pm5) }{2\sqrt{3} }$

$x=\frac{1\pm5 }{\sqrt{3} }$

⇒  $x=\frac{1+5 }{\sqrt{3} }$  or  $x=\frac{1-5 }{\sqrt{3} }$

⇒  $x=\frac{6 }{\sqrt{3} }$   or  $x=\frac{-4 }{\sqrt{3} }$

⇒  $x=2{\sqrt{3} }$  or  $x=\frac{-4 }{\sqrt{3} }$

Answer 2

Given,

A quadratic equation √3x²-2x-8√3 = 0

To Find,

The solution of this equation.

Solution,

By using the middle term splitting method,

√3x²-2x-8√3 = 0

Splitting -2x an -6x+4x

So, we get

√3x²-6x+4x-8√3 = 0

√3x(x-2√3)-4(x+2√3) = 0

(x-2√3)(√3x-4) = 0

So, x = 2√3 or 4/√3

Hence the solution of the equation √3x²-2x-8√3 = 0 is x = 2√3 or 4/√3.