Question

A = √28 - √20 totul supra √3+1
B= √12 +2 totul supra √7 -√5
Calculati media geometrica a nr a si b

Answer 1

[tex]A= \frac{ \sqrt{28}- \sqrt{20} }{ \sqrt{3} +1} \\ A= \frac{ 2\sqrt{7}-2 \sqrt{5} }{ \sqrt{3}+1 } \\ A= \frac{2( \sqrt{7}- \sqrt{5}) }{ \sqrt{3}+1 } \\ A= \frac{2( \sqrt{7} - \sqrt{5 })( \sqrt{3}-1) }{2} \\ [/tex]
2 cu doi se implifica si iti va da:
A=(√7-√5)(√3-1)
[tex]B= \frac{ \sqrt{12}+2 }{ \sqrt{7}- \sqrt{5} } \\ B= \frac{2 \sqrt{3}+2 }{ \sqrt{7}- \sqrt{5} } \\ B= \frac{2( \sqrt{3}+1) }{ \sqrt{7}- \sqrt{5} } \\ B= \frac{2( \sqrt{3}+1)( \sqrt{7}+ \sqrt{5)} }{2} [/tex]
2 cu 2 se simplifica si vom avea:
B=(√3+1)(√7+√5)
[tex]mg= \sqrt{A*B} \\ mg= \sqrt{ (\sqrt{7}- \sqrt{5})(\sqrt{3}-1)( \sqrt{3}+1)( \sqrt{7}+ \sqrt{5}) } [/tex]
Si acum faci diferenta de patrate:
[tex]mg= \sqrt{(7-5)(3-1)} \\ mg= \sqrt{2*2} [/tex]⇒$mg=2$