Question

patricia says that it's more appropriate to use the method of factoring than extracting square roots in solving 4x2^-9=0. do you agree with patricia? explain your answer

Answer 1

`1^(o) \\ \\ 4x^(2)-9=0 \\ \\ (2x-3)(2x+3)=0 \\ \\ 2x-3=0 \ \vee \ 2x+3=0 \\ \\ 2x=3 \ \vee \ 2x=-3 \\ \\ x= (3)/(2) \ \vee \ x=- (3)/(2) \\ \\ 2^(o) \\ \\ 4x^(2)-9=0 \\ \\ 4x^(2)=9 \\ \\ x^(2)= (9)/(4) \\ \\ x= \sqrt{ (9)/(4) } \ \vee \ -\sqrt{ (9)/(4) } \\ \\ x= (3)/(2) \ \vee \ x=- (3)/(2) \\ \\ 3^(o) \\ \\ 4x^(2)-9=0 \\ \\ \Delta=0^(2)-4*4*(-9)=144 \\ \\ √(\Delta) =12 \\ \\ x_(1)= (0+12)/(8) = (3)/(2)`


`x_(2)= (0-12)/(8) =- (3)/(2)`