Question

[Cường Hoàng]

Bài 1: Tính: a, \(\sqrt{27}+\sqrt{75}-\sqrt{\dfrac{1}{3}}\)

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

Bài 2: Rút gọn: A= \(\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{a}}\right):\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\)

Bài 3: A= \(\dfrac{2x^3+x^2+2x+4}{2x+1}\)

a, Tìm x ϵ Z để A ϵ Z

Các bạn giúp mình với được không? Mình cảm ơn!

Answer 1

[Mysterious Person]

1) a) \(\sqrt{27}\) + \(\sqrt{75}\) - \(\sqrt{\dfrac{1}{3}}\) = \(3\sqrt{3}\) + \(5\sqrt{3}\) - \(\dfrac{\sqrt{3}}{3}\) = \(8\sqrt{3}\) - \(\dfrac{\sqrt{3}}{3}\)

= \(\dfrac{23\sqrt{3}}{3}\)

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

= \(\sqrt{\left(\sqrt{3}\right)^2+2.\sqrt{3}.1+1^2}\) \(-\sqrt{\left(\sqrt{3}\right)^2-2.\sqrt{3}.1+1^2}\)

= \(\sqrt{\left(\sqrt{3}+1\right)^2}\) \(-\sqrt{\left(\sqrt{3}-1\right)^2}\)

= \(\left(\sqrt{3}+1\right)\) \(-\left(\sqrt{3}-1\right)\)

= \(\sqrt{3}+1-\sqrt{3}+1\)

= 2

Answer 2

[Mysterious Person]

2) \(\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{a}}\right)\) : \(\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\)

= \(\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right)\) : \(\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)

= \(\left(\dfrac{a-1}{\left(\sqrt{a}-1\right)\sqrt{a}}\right)\) : \(\left(\dfrac{\left(\sqrt{a}-1\right)+2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)

= \(\left(\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\sqrt{a}}\right)\) : \(\left(\dfrac{\left(\sqrt{a}-1\right)+2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)

= \(\dfrac{\sqrt{a}+1}{\sqrt{a}}\) : \(\dfrac{2}{\sqrt{a}+1}\) = \(\dfrac{\sqrt{a}+1}{\sqrt{a}}\) . \(\dfrac{\sqrt{a}+1}{2}\) = \(\dfrac{\left(\sqrt{a}+1\right)^2}{2\sqrt{a}}\)