Question

Por favoor, podem me ajudar?!!

Em cada item,fatore o 1 membro e depois resolva a equação-produto resultante:

a) 5x² - 15x = 0

b) n² - 121 = 0

c) t² + 12t + 36= 0

d) 3x³ - 48x = 0

Answer 1

$a) ~~5x^2 - 15x = 0\to\\\\ 5x(x-3)=0\to\\\\ 5x=0\to~~x= \dfrac{0}{5} \to~~\boxed{x=0}\\\\x-3=0\to~~\boxed{x=3}\\\\\\ \large\boxed{\boxed{S=\{0~;~3\}}}$




$b)~~n^2 - 121 = 0\to\\\\ n^2=121\to\\\\ n=\pm~ \sqrt{121} \to\\\\ \boxed{n=\pm~11}\\\\\\ \large\boxed{\boxed{S=\{-11~;~11\}}}$




$c)~~ t^2 + 12t + 36= 0 \to\\\\(t+6)(t+6)=0\to\\\\ t+6=0\to~~\boxed{t'=t''=-6}\\\\\\ \large\boxed{\boxed{S=\{-6\}}}$




$d) ~~3x^3- 48x = 0\to\\\\ 3x(x^2-16)=0\to\\\\ 3x=0\to~~x= \dfrac{0}{3} \to~~\boxed{x=0}\\\\ x^2-16=0\to ~~ x^2=16\to~~ x=\pm~ \sqrt{16} \to~~\boxed{x=\pm~4 }\\\\\\ \large\boxed{\boxed{S=\{-4~;~0~;~4\}}}$