Question

f:R => Rf(x) = x² + 2
f(a) + f(a+1)=5
a = ?

Answer 1

Răspuns:

Explicație pas cu pas:

f(a) = a^2 + 2

f(a + 1) = (a + 1)^2 + 2 = a^2 + 2a + 1 + 2 = a^2 + 2a + 3

_______

a^2 + 2 + a^2 + 2a + 3 = 5

3a^2 + 5 = 5

3a^2 = 5 - 5 = 0

a^2 = 0

a = 0

Answer 2

$\displaystyle f:\mathbb{R}\rightarrow \mathbb{R},~f(x)=x^2+2\\\\ f(a)+f(a+1)=5,~a=?\\\\ f(a)=a^2+2\\\\ f(a+1)=(a+1)^2+2=a^2+2 \cdot a \cdot 1+1^2+2=a^2+2a+1+2=\\\\=a^2+2a+3\\\\ f(a)+f(a+1)=5 \Rightarrow a^2+2+a^2+2a+3=5 \Rightarrow 2a^2+2a+5-5=0 \Rightarrow \\\\ \Rightarrow 2a^2+2a=0 \Rightarrow 2a(a+1)=0 \Rightarrow 2a=0 \Rightarrow a=\frac{0}{2} \Rightarrow a=0\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow a+1=0 \Rightarrow a=0-1 \Rightarrow a=-1\\\\ a=0;~a=-1$