Question

Aratati ca ecuatiile urmatoare sunt echivalente:
a)x(2x+1)+(x+1)(x+2)=2(x²+11)+1
b)2(x+1)²-(x-2)(x+2)=27

Answer 1

Echivalent=solutii egale
a) 2x²+x+x²+2x+x+2=2x²+22+1⇒3x²+4x+2=2x²+23⇒3x²+4x+2-2x²-23=0⇒x²+4x-21=0⇒x²+7x-3x-21=0⇒x(x+7)-3(x+7)=0⇒(x+7)(x-3)=0