Question

Đưa về hằng đẳng thức các biểu thức sau:

a) 19+8√3

b)11-4√6

c)9-4√2

d)21+6√10

e)23+6√10

f)49-20√6

Answer 1

Answer 2

a) \(19+8\sqrt{3}=3+2\sqrt{3}\cdot4+16=\left(\sqrt{3}+4\right)^2\)

b) \(11-4\sqrt{6}=3-2\sqrt{3}\cdot2\sqrt{2}+8=\left(\sqrt{3}-2\sqrt{2}\right)^2\)

c) \(9-4\sqrt{2}=8-2\cdot2\sqrt{2}+1=\left(2\sqrt{2}-1\right)^2\)

d) \(21+6\sqrt{10}=18+2\cdot3\sqrt{2}\cdot\sqrt{5}+5-2=\left(3\sqrt{2}+\sqrt{5}\right)^2-\left(\sqrt{2}\right)^2\)

e) \(23+6\sqrt{10}=18+2\cdot3\sqrt{2}\cdot\sqrt{5}+5=\left(3\sqrt{2}+\sqrt{5}\right)^2\)

f) \(49-20\sqrt{6}=\left(5\sqrt{2}\right)^2-2\cdot5\sqrt{2}\cdot2\sqrt{3}+\left(2\sqrt{3}\right)^2-13=\left(5\sqrt{2}-2\sqrt{3}\right)^2-\left(\sqrt{13}\right)^2\)