Question

Media geometrica a nr a=(√3-√2) (√9-√5) si b=(√3+√2) (√9+√5) ​

Answer 1

Răspuns:

2

Explicație pas cu pas:

folosim formula de calcul prescurtat a diferentelor de patrate:

a^2 - b^2 = (a-b)(a+b)

Mg = rad(a.b) = rad[(√3-√2) (√9-√5)(√3+√2) (√9+√5)] =

rad[ (√3-√2)(√3+√2) (√9-√5)(√9+√5)] =

rad[(3-2)(9-5)] =

rad4 =

2.

Answer 2

$\it m_g=\sqrt{a\cdot b}=\sqrt{(\sqrt3-\sqrt2)(\sqrt9-\sqrt5)(\sqrt3+\sqrt2)(\sqrt9+\sqrt5)}=\\ \\ \\ =\sqrt{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)(\sqrt9-\sqrt5)(\sqrt9+\sqrt5)} =\sqrt{\[[(\sqrt3)^2-(\sqrt2)^2}]\[[(\sqrt9)^2-(\sqrt5)^2]}$$\it =\sqrt{1\cdot4}=\sqrt4=2$