Question

 1.(√2 + 1)^3 − (√2 − 1)^3 

 2.√13 − √160 − √53 + 4√90

 3.(√3 + 1)^3 − (√3 − 1)^3

Answer 1

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

( \(\sqrt{2}\) +1- \(\sqrt{2}\) +1)[( \(\sqrt{2}\) +1)^2+( \(\sqrt{2}\) -1)( \(\sqrt{2}\) +1)+(\(\sqrt{2}\) -1)^2]

=2( 2+\(2\sqrt{2}\)+1+2-1+2-\(2\sqrt{2}\)+1)=2.7=14

Answer 2

2) \(\sqrt{13}\)-\(\sqrt{160}\)-\(\sqrt{53}\)+\(4\sqrt{90}\)

=\(\sqrt{13}\)-\(4\sqrt{10}\)-\(\sqrt{53}\)+\(12\sqrt{10}\)=\(\sqrt{13}\)-\(\sqrt{53}\)+\(16\sqrt{10}\)=

hình như sai đề rồi

Answer 3

3) tương tự bài 1)

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

( \(\sqrt{3}\) +1- \(\sqrt{3}\) +1)[( \(\sqrt{3}\) +1)^2+( \(\sqrt{3}\) -1)( \(\sqrt{3}\) +1)+(\(\sqrt{3}\) -1)^2]

=2( 3++1+3-1+3-\(2\sqrt{3}\)+1)=2.10=20