Thực hiện phép tính $\frac{4}{\sqrt{7}-\sqrt{3}}$ + $\frac{6}{3+\sqrt{3}}$ +$\frac{\sqrt{7}-7}{\sqrt{7}-1}$ 04/09/2021 Bởi Adalyn Thực hiện phép tính $\frac{4}{\sqrt{7}-\sqrt{3}}$ + $\frac{6}{3+\sqrt{3}}$ +$\frac{\sqrt{7}-7}{\sqrt{7}-1}$
$A = \dfrac{4(\sqrt{7} + \sqrt{3})}{(\sqrt{7} – \sqrt{3})(\sqrt{7} + \sqrt{3})} + \dfrac{6(3 – \sqrt{3})}{\sqrt{3}(3 + \sqrt{3})(3 – \sqrt{3})} – \dfrac{\sqrt{7}(\sqrt{7} – 1)}{\sqrt{7} – 1}$ $A = \sqrt{7} + \sqrt{3} + 3 – \sqrt{3} – \sqrt{7} =3$ Bình luận
Giải thích các bước giải: $\dfrac{4}{\sqrt{7} – \sqrt{3}} + \dfrac{6}{3 + \sqrt{3}} + \dfrac{\sqrt{7} – 7}{\sqrt{7} – 1}$ $= \dfrac{4\left ( \sqrt{7} + \sqrt{3} \right )}{\left ( \sqrt{7} – \sqrt{3} \right )\left ( \sqrt{7} + \sqrt{3} \right )} + \dfrac{6\left ( 3 – \sqrt{3} \right )}{\left ( 3 + \sqrt{3} \right )\left ( 3 – \sqrt{3} \right )} – \dfrac{\sqrt{7}\left ( \sqrt{7} – 1 \right )}{\sqrt{7} – 1}$ $= \sqrt{7} + \sqrt{3} + 3 – \sqrt{3} – \sqrt{7}$ $= 3$ Bình luận
$A = \dfrac{4(\sqrt{7} + \sqrt{3})}{(\sqrt{7} – \sqrt{3})(\sqrt{7} + \sqrt{3})} + \dfrac{6(3 – \sqrt{3})}{\sqrt{3}(3 + \sqrt{3})(3 – \sqrt{3})} – \dfrac{\sqrt{7}(\sqrt{7} – 1)}{\sqrt{7} – 1}$
$A = \sqrt{7} + \sqrt{3} + 3 – \sqrt{3} – \sqrt{7} =3$
Giải thích các bước giải:
$\dfrac{4}{\sqrt{7} – \sqrt{3}} + \dfrac{6}{3 + \sqrt{3}} + \dfrac{\sqrt{7} – 7}{\sqrt{7} – 1}$
$= \dfrac{4\left ( \sqrt{7} + \sqrt{3} \right )}{\left ( \sqrt{7} – \sqrt{3} \right )\left ( \sqrt{7} + \sqrt{3} \right )} + \dfrac{6\left ( 3 – \sqrt{3} \right )}{\left ( 3 + \sqrt{3} \right )\left ( 3 – \sqrt{3} \right )} – \dfrac{\sqrt{7}\left ( \sqrt{7} – 1 \right )}{\sqrt{7} – 1}$
$= \sqrt{7} + \sqrt{3} + 3 – \sqrt{3} – \sqrt{7}$
$= 3$