Question

Thực hiện phép tính sau:

a.(1+√2-√3)(1+√2+√3)

b.(1+2√3-√2)(1+2√3+√2)

c.(2√27-3√48+3√75-√192)(1-√3)

Cảm ơn các bạn ạ😘😍

Answer 1

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

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

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

\(=2\sqrt{2}\)

Answer 2

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

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

\(=1+4\sqrt{3}+12-2\)

\(=9+4\sqrt{3}\)

Answer 3

\(c,\left(2\sqrt{27}-3\sqrt{48}+3\sqrt{75}-\sqrt{192}\right)\left(1-\sqrt{3}\right)\)

\(=\left(6\sqrt{3}-12\sqrt{3}+15\sqrt{3}-8\sqrt{3}\right)\left(1-\sqrt{3}\right)\)

\(=\left[\sqrt{3}\left(6-12+15-8\right)\right]\left(1-\sqrt{3}\right)\)

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

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