Question

Rezolvati ecuatiile
a)(2x-1) la puterea a 2 a - ( x+2) la puterea a 2a=25

Answer 1

(2x-1)^2-(x+2)^2=25

ai formulele:

(a+b)^2=a^2+2ab+b^2

(a-b)^2=a^2-2ab+b^2

4x^2-4x+1-(x^2+4x+4)=25

4x^2-4x+1-x^2-4x-4=25

3x^2-8x-3=25

3x^2-8x-28=0

a=3

b= -8

c= -28

delta=b^2-4ac

=64 - 4 ori 3 ori (-28)

=64 - 12 ori (-28)

=64 + 336

=400

notam radical din delta cu d ==> d= radical din 400 = 20

x1 = (-b-d)/2a = (8-20)/6 = -12/6 = -2

x2 = (-b+d)/2a = (8+20)/6 = 28/6 = 14/3