Question

Aflati solutia ecuatiilor
a) (x-5)(x+5)-(x-3)^2=x-9
b) (x+2)^2-x(x+5)=2(x-7)
c) √(x+1)^2=3. Radicalul cuprinde totul pana la egal
d) 2(x+2)+√x^2-4x+4=2x+9 radicalul cuprinde totul pana la egal

Answer 1

[tex]a) (x-5)(x+5)-(x-3)^2=x-9\\ x^{2} -5^2-( x^{2} -6x+9)=x-9\\ x^{2} -25- x^{2} +6x-9-x+9=0\\ 5x-25=0\\5x=25\\x=25:5\\x=5\\ b) (x+2)^2-x(x+5)=2(x-7)\\ x^{2} +4x+4- x^{2} -5x=2x-14\\ -x-2x=-14-4\\ -3x=-18\\ x=(-18):(-3)\\ x=6\\ c) \sqrt{(x+1)^2}=3\\x+1=3\\x=3-1\\x=2\\ d) 2(x+2)+ \sqrt{ x^{2} -4x+4}=2x+9\\ 2x+4+ \sqrt{(x-2)^2} =2x+9\\ 2x+4+x-2=2x+9\\ 3x-2x=9-4+2\\ x=7[/tex]