Question

Daca a si b sunt numere naturale astfel a+b = 2√2 si a*b=2 calculati  1/a + 1/b si a²+b²

Answer 1

$\it \dfrac{1}{a} + \dfrac{1}{b} =\dfrac{b+a}{ab} =\dfrac{2\sqrt2}{2} =\sqrt2$

$\it a^2+b^2 =(a+b)^2 -2ab =(2\sqrt2)^2-2\cdot2=4\cdot2-4=4$