Question

${\displaystyle x^2+3\sqrt{3}-30=0}$ 

Answer 1

We write, ${\displaystyle 3\sqrt{3}x=5\sqrt{3}x-2\sqrt{3}x as x^2\times (-30)=-30x^2=5\sqrt{3}x x(-2\sqrt{3}x)}$  

∴${\displaystyle x^2+3\sqrt{3}x-30=0}$ 

⇒${\displaystyle x^2+5\sqrt{3}x-2\sqrt{3}x-30=0}$ 

⇒ ${\displaystyle x(x+5\sqrt{3})-2\sqrt{3}(x+5\sqrt{3})=0}$ 

⇒${\displaystyle (x+5\sqrt{3})(x-2\sqrt{3})=0}$ 

⇒${\displaystyle x+5\sqrt{3}=0 \text{or} x-2\sqrt{3}=0}$ 

⇒${\displaystyle x=-5\sqrt{3} \text{or} x=2\sqrt{3}}$ 

Hence, the roots of the given equation are ${\displaystyle -5\sqrt{3}}$ and ${\displaystyle 2\sqrt{3}}$