Question

4x² +4√3x-3=0 by factorization me5hid​

Answer 1

✪ᴀɴsᴡᴇʀ✪

$\:\:\:\:\:x = \frac{-\sqrt{3} +\sqrt{6}}{2}</p><p>\:or\: \frac{-\sqrt{3} - \sqrt{6}} {2}$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

The given equation is

$\:\:\:\:\:\:\:\:\:\:\:\:\:4x^2 + 4\sqrt{3}x - 3 = 0$

It is not possible to factorize the expression by splitting middle term. However it can be factorize and solve as follows.

$\implies {2x}^2 + 2.2x. \sqrt{3}+ {\sqrt{3}}^2$

$\:\:\:\:\:\:\:\:\:\: - {\sqrt{3}}^2- 3 = 0$

$\implies {(2x + \sqrt{3})}^2- 3 - 3 = 0$

$\implies {(2x + \sqrt{3})}^2- {\sqrt{6}}^2= 0$

$\implies (2x + \sqrt{3}- \sqrt{6})$

$\:\:\:\:\:\:\:\:\:\:\:(2x + \sqrt{3} + \sqrt{6}) = 0$

$\implies (2x + \sqrt{3}- \sqrt{6}) =0$

$\:\:\:\:\:\:or\:(2x + \sqrt{3} + \sqrt{6}) = 0$

$\implies x = \frac{-\sqrt{3} +\sqrt{6}}{2 }$

$\:\:\:\:\:or\: x = \frac{-\sqrt{3} - \sqrt{6}} {2}$