2x^2 6x+3=0 ⇒ 2(x^2 3x+32)=0 ⇒x^2 3x+32=0 ⇒x^2 3x+32=0 ⇒x^2 2×32x+94 94+32=0 ⇒(x 32)^2=94 32 ⇒(x 32)^2=9 64 ⇒(x 32)^2=34 ...

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Exponential Representation for Irrational Numbers

Solve 2x2-6x...

Question

Solve
$2 x^{2} - 6 x + 3 = 0$

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Solution

$2 x^{2} - 6 x + 3 = 0$
$\Rightarrow 2 (x^{2} - 3 x + \frac{3}{2}) = 0$
$\Rightarrow x^{2} - 3 x + \frac{3}{2} = 0$
$\Rightarrow x^{2} - 3 x + \frac{3}{2} = 0$
$\Rightarrow x^{2} - 2 \times \frac{3}{2} x + \frac{9}{4} - \frac{9}{4} + \frac{3}{2} = 0$
$\Rightarrow {(x - \frac{3}{2})}^{2} = \frac{9}{4} - \frac{3}{2}$
$\Rightarrow {(x - \frac{3}{2})}^{2} = \frac{9 - 6}{4}$
$\Rightarrow {(x - \frac{3}{2})}^{2} = \frac{3}{4}$
$\Rightarrow x - \frac{3}{2} = \pm \frac{\sqrt{3}}{2}$
$∴ x = \frac{3 \pm \sqrt{3}}{2}$

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