a) x² + 12x + 36 = 0
⇔ x² + 2.x.6 + 6² =0
⇔ (x + 6)² =0
⇔ x + 6 = 0
⇔ x = -6
b) 81.x² - 625 =0
⇔ 81.x² = 625
⇔ x² = $\frac{625}{81}$
⇔ \(\left[ \begin{array}{l}x=\sqrt{\frac{625}{81}}= \frac{25}{9} \\x=-\sqrt{\frac{625}{81}}= -\frac{25}{9}\end{array} \right.\)
c) x³ + 6.x² + 12x + 8 = 0
⇔ (6.x² + 12x) + (x³ + 8) = 0
⇔ 6x(x + 2) + (x + 2).(x² - 2x + 4) = 0
⇔ (x + 2).(x² - 2x + 6x + 4 ) = 0
⇔ (x + 2).(x² + 4x +4) =0
⇔ (x + 2).(x + 2)² = 0
⇔ (x + 2)³ = 0
⇔ x + 2 = 0
⇔ x = -2
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