Question

aratati ca expresia e(x)= (x+2)^2+(2x-1)^2 supra (x-3)^1+(3x+1)^2 are valoare constanta pentru orice nr real x.

Answer 1

E(x)=[(x+2)²+(2x-1)²]/[(x-3)²+(3x+1)²]=
=(x²+4x+4+4x²-4x+1)/(x²-6x+9+9x²+6x+1)=
=(5x²+5)/(10x²+10)=
=5(x²+1)/10(x²+1)=
=5/10=1/2