Question

Se ştie că A + 1/A=2. Calculați A^2+1/A^2

Answer 1

$\left(A+\dfrac{1}A\right)^2=A^2+2A\dfrac{1}A+\dfrac{1}{A^2},\ deci\ A^2+\dfrac{1}{A^2}=\left(A+\dfrac{1}A\right)^2-2=2^2-2=2.$

Simplu, nu ? :-).

Green eyes.

Answer 2

a+1/a=2
a²+1=2a
a²-2a+1=0
(a-1)²=0
a=1
a²+1/a²=2 
sau
a²+1/a²=(a+1/a)²-2=4-2=2