Question

Daca a/b=7-4 radical din 3, calculati a^2+b^2 totul supra a*b

Answer 1

Salut,

$\dfrac{b}a=\dfrac{1}{7-4\cdot\sqrt3}=\dfrac{1}{\sqrt{49}-\sqrt{48}}=\dfrac{\sqrt{49}+\sqrt{48}}{(\sqrt{49}+\sqrt{48})(\sqrt{49}-\sqrt{48})}=\\\\\\=\dfrac{\sqrt{49}+\sqrt{48}}{49-48}=7+4\sqrt3.\ Deci:\ \dfrac{a^2+b^2}{ab}=\dfrac{a}b+\dfrac{b}a=7-4\sqrt3+7+4\sqrt3=14.$

Green eyes.