Question

solve the equation 9 x square - 15 X + 6 is equal to 0 by using perfect square method

Answer 1

Given Equation is 9x^2 - 15x + 6 = 0

 = > $x^2 - \frac{15x}{9} + \frac{6}{9} = 0$

= > $x^2 - \frac{5x}{3} + \frac{2}{3} = 0$

= > $x^2 - \frac{5x}{3} = - \frac{2}{3}$

Add (5/6)^2 on both sides, we get

= > $x^2 - \frac{5x}{3} + ( \frac{5}{6})^2 = - \frac{2}{3} + ( \frac{5}{6} )^2$

= > $(x - \frac{5}{6} )^2 = - \frac{2}{3} + \frac{25}{36}$

= > $(x - \frac{5}{6} )^2 = \frac{-24 + 25}{36}$

= > $(x - \frac{5}{6} )^2 = \frac{1}{36}$

= > $x - \frac{5}{6} = \frac{1}{6}$

= > $x = \frac{5}{6} + \frac{1}{6}$

= > x = 1.



Now,

= > $x - \frac{5}{6} = -\frac{1}{6}$

= > $x = - \frac{1}{6} + \frac{5}{6}$

= > $x = \frac{4}{6}$

= > x = $\frac{2}{3}$


Therefore x = 1, 2/3.


Hope this helps!