c)(x+2)(x+4)=(x-5)(x-3)
x²+6x+8=x²-8x+15
6x+8x=15-8
14x=7 =>x=7/14=1/2
d)2x=(5-4√3)(5+4√3)
2x=25-48
2x=-23 =>x=-23/2
e)Intai rationalizam fiecare termen in parte, adica primul se inmulteste cu √3, al doilea cu (√3-1) si al treilea cu (√3+1)
[tex] \frac{ \sqrt{3}x }{3} - \frac{( \sqrt{3}+1) ^{2} }{2} = \frac{( \sqrt{3} -1) ^{2} }{2} [/tex]
Aducem la numitor comun (6)
[tex] \frac{2 \sqrt{3} x}{6} - \frac{3(3+2 \sqrt{2} +1)}{6} = \frac{3(3-2 \sqrt{2} +1)}{6} [/tex]
[tex] 2\sqrt{3} x-12-6 \sqrt{3} =12-6 \sqrt{3} [/tex]
[tex]2 \sqrt{3} x=24 =\ \textgreater \ x= \frac{24}{2 \sqrt{3} } = \frac{24 \sqrt{3} }{2*3} =4 \sqrt{3} [/tex]
