Question

a+b=$2 \sqrt{2}$
a*b=2
calculati : $\frac{1}{a}+ \frac{1}{b}$ si $a^{2} + b^{2}$

Answer 1

$\rm a+b=2\sqrt2 \\ \\ ab=2 \\ \\ \\ \\ Pentru~punctul~2~folosesti~formula: \\ \\ (a+b)^2=a^2+2ab+b^2 \\ \\ (2\sqrt2)^2=a^2+2\cdot2+b^2 \\ \\ 8=a^2+4+b^2 \Longrightarrow \bold{a^2+b^2=4}$




$\rm ^{b)}\frac1a+^{a)}\frac1b = \frac{b}{ab}+\frac{a}{ab} \\ \\ \frac{a+b}{ab}= \frac{\not2\sqrt2}{\not2}=\bold{\sqrt2}$