Question

Formula radicalilor compusi(clasa 7)

Answer 1

Avem urmatorul radical de forma:
$\sqrt{a+\sqrt{b}} \\ a = a \\ b = b \\ c = \sqrt{a^2-b}$

Atunci avem formula radicalilor compusi:
$\sqrt{a+\sqrt{b}}=\sqrt{\frac{a+c}{2}}+\sqrt{\frac{a-c}{2}}$
Daca avem radicalul acesta:
$\sqrt{a-\sqrt{b}}$

Formula radicalilor compusi este aceasta:
$\sqrt{a-\sqrt{b}}=\sqrt{\frac{a+c}{2}}-\sqrt{\frac{a-c}{2}}$

Answer 2

$\sqrt{A+ \sqrt{B}}= \sqrt\frac{A+C}{2}+ \sqrt\frac{A-C}{2} \sqrt{A- \sqrt{B}}= \sqrt\frac{A+C}{2}- \sqrt\frac{A-C}{2} unde C^{2}=A^{2}-B$