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

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

$x_{2}= \frac{0-12}{8} =- \frac{3}{2}$