Question

a) \(\frac{1}{\sqrt{5}-1}\) + \(\frac{1}{1+\sqrt{5}}\)

b) \(\frac{4}{1+\sqrt{3}}\) - \(\frac{2}{2-\sqrt{3}}\)

c) \(\frac{2}{\sqrt{5}+\sqrt{3}}\) - \(\frac{3-\sqrt{15}}{\sqrt{5}-\sqrt{3}}\)

Answer 1

c. \(\frac{2}{\sqrt{5}+\sqrt{3}}-\frac{3-\sqrt{15}}{\sqrt{5}-\sqrt{3}}\)

= \(\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\frac{\left(3-\sqrt{15}\right)\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}\)

= \(\frac{2\sqrt{5}-2\sqrt{3}}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\frac{3\sqrt{5}+3\sqrt{3}-5\sqrt{3}+3\sqrt{5}}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}\)

= \(\frac{2\sqrt{5}-2\sqrt{3}-3\sqrt{5}+3\sqrt{3}-5\sqrt{3}+3\sqrt{5}}{5-3}\)

= \(\frac{2\sqrt{5}-2\sqrt{3}-2\sqrt{3}}{2}\)

= \(\frac{2\sqrt{5}-4\sqrt{3}}{2}\)

mk chỉ bik cách lm như z thoy còn kết quả thì mk chưa chắc đã đúng đâu nên pn xem lại nhá

Answer 2

\(\frac{1}{\sqrt{5}-1}+\frac{1}{1+\sqrt{5}}\)

= \(\frac{1}{\sqrt{5}-1}-\frac{1}{\sqrt{5}+1}\)

= \(\frac{\sqrt{5}+1}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}-\frac{\sqrt{5}-1}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}\)

= \(\frac{\sqrt{5}+1}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}-\frac{\sqrt{5}+1}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}\)

= \(\frac{2}{5-1}\)

= \(\frac{2}{4}\)

= \(\frac{1}{2}\)

Answer 3

những câu khác tương tự