Answer: x = - 2√5, √5/3
Step-by-step explantion
3 √ 5 x 2 + 25 x − 10 √ 5 = 0 35x2+25x−105=0
⇒ 3√5x2 + 30x – 5x – 10√5 = 0
⇒ 3√5x(x + 2√5) – 5(x + 2√5) = 0
⇒ (x + 2√5)(3√5x – 5) = 0
x = - 2√5, √5/3
[tex]3 \sqrt{5} {x}^{2} + 25x - 10 \sqrt{5} = 0 \\ \\ 3 \sqrt{5} {x}^{2} + 30x - 5x - 10 \sqrt{5} = 0 \\ \\ 3x( \sqrt{5} x + 10) - \sqrt{5} ( \sqrt{5} + 10) = 0 \\ \\ ( \sqrt{5} x + 10)(3x - \sqrt{5} ) = 0[/tex]
[tex] \sqrt{5} x + 10 = 0 \\ \\ \sqrt{5}x = - 10 \\ \\ x = \frac{ - 10}{ \sqrt{5} } \\ \\ x = \frac{ - 2 \times \sqrt{5 } \times \sqrt{5} }{ \sqrt{5} } \\ \\ x = - 2 \sqrt{5} .[/tex]
[tex]3x - \sqrt{5} = 0 \\ \\ 3x = \sqrt{5} \\ \\ x = \frac{ \sqrt{5} }{3} .[/tex]
The values of x are -2√5 & √5/3 .
