Question

Se consideră funcţia f(x) =x^2 + 2 . Determinaţi numerele reale a pentru care f(a) + f (a+1)=5

Answer 1

 

$\displaystyle\\f(x)=x^2+2\\\\f(a)=a^2+2\\\\f(a+1)=(a+1)^2+2\\\\f(a)+f(a+1)=5\\\\a^2+2+(a+1)^2+2=5\\\\a^2+2+a^2+2a+1+2=5\\\\a^2+a^2+2a+2+1+2=5\\\\2a^2+2a+5=5\\\\2a^2+2a=5-5\\\\2a^2+2a=0\\\\2(a^2+a)=0\\\\a^2+a=0\\\\a(a+1)=0\\\\\\\boxed{\bf a_1=0}\\\\a+1=0\\\boxed{\bf a_2=-1}$

.