Question

Khai triển:

a) (2+√3)²

b) (√7-3)²

c) (5+√2)²

d) (√11-5)²

e) (1+√5)² + (3-√5)²

f) (2+√7)² + (√7-3)²

Answer 1

a) \(\left(2+\sqrt{3}\right)^2=4+4\sqrt{3}+3=7+4\sqrt{3}\)

b) \(\left(\sqrt{7}-3\right)^2=7-6\sqrt{7}+9=16-6\sqrt{7}\)

c) \(\left(5+\sqrt{2}\right)^2=25+10\sqrt{2}+2=27+10\sqrt{2}\)

d) \(\left(\sqrt{11}-5\right)^2=11-10\sqrt{11}+25=36-10\sqrt{11}\)

e) \(\left(1+\sqrt{5}\right)^2+\left(3-\sqrt{5}\right)^2=1+2\sqrt{5}+5+9-6\sqrt{5}+5=20-4\sqrt{5}\)

f) \(\left(2+\sqrt{7}\right)^2+\left(\sqrt{7}-3\right)^2=4+4\sqrt{7}+7+7-6\sqrt{7}+9=27-2\sqrt{7}\)