Question

Rationalizeaza următoarele fracții ​

Answer 1

Răspuns:

Explicație pas cu pas:

prima fractie  - amplifici cu √12

-4√3*√12/√12*√12 = -4√36/12 = -4*6/12 = -24/12 = -2

a doua fractie - amplifici cu √3 + 1

(√3 + 1) / (√3 - 1)(√3 + 1) = (√3 + 1)/(3 - 1) = (√3 + 1)/2

a treia fractie - amplifici cu √2 + 1

(√2 + 1)(√2 + 1)/(√2 - 1)(√2 + 1) = (2 + 2√2 + 1)/(2 - 1) = 3 + 2√2

Answer 2

$\it -\dfrac{4\sqrt3}{\sqrt{12}}=-\dfrac{4\sqrt3}{\sqrt{4\cdot3}}=-\dfrac{4\sqrt3}{2\sqrt3}=-2\\ \\ \\ \dfrac{^{\sqrt3+1)}1}{ \ \sqrt3-1}=\dfrac{\sqrt3+1}{(\sqrt3-1)(\sqrt3+1)}=\dfrac{\sqrt3+1}{(\sqrt3)^2-1^2}=\dfrac{\sqrt3+1}{3-1}=\dfrac{\sqrt3+1}{2}$

$\dfrac{^{\sqrt2+1)}\sqrt2+1}{\ \sqrt2-1}=\dfrac{(\sqrt2+1)^2}{(\sqrt2)^2-1^2}=\dfrac{(\sqrt2)^2+2\sqrt2+1}{2-1}=\dfrac{2+2\sqrt2+1}{1} = 3+2\sqrt2$