✅ Corrigé — Exercice 3

1) (2x+3)² = 4x²+12x+9.
2) (x−5)² = x²−10x+25.
3) (3x+1)(3x−1) = 9x²−1.

4) x²+8x+16 = (x+4)².
5) x²−10x+25 = (x−5)².
6) 9x²−4 = (3x−2)(3x+2).

✅ Corrigé — Exercice 4

1) x²−7x+12 = 0. Δ = 49−48 = 1. x₁=(7−1)/2=3 ; x₂=(7+1)/2=4.
2) x²+4x+4 = 0. Δ = 16−16 = 0. x₀ = −4/2 = −2 (racine double).
3) x²+2x+5 = 0. Δ = 4−20 = −16 < 0 → pas de solution réelle.