Explicație pas cu pas:
[tex]a + b = 2 \sqrt{2} \\ a \times b = 2 \\ \frac{1}{a} + \frac{1}{b} = \frac{a + b}{a \times b} = \frac{2 \sqrt{2} }{2} = \sqrt{2} \\ a {}^{2} + b {}^{2} = (a + b) {}^{2} - 2(a \times b )= \\ (2 \sqrt{2} ) {}^{2} - 2 \times 2 = 8 - 4 = 4[/tex]
