Question

thực hiện pháp tính , rút gọn các biểu thức sau :

\(A=\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)\)

B=\(\left(\sqrt{45}+\sqrt{63}\right)\left(\sqrt{7}-5\right)\)

C=\(\left(\sqrt{5}+\sqrt{3}\right)\left(5-\sqrt{15}\right)\)

Answer 1

A= \(\sqrt{5}^2-2^2=5-4=1\)
B=(\(\sqrt{9}\cdot\sqrt{5}+\sqrt{9}\cdot\sqrt{7}\) )(\(\sqrt{7}-\sqrt{5}\))
=\(\sqrt{9}\left(\sqrt{5}+\sqrt{7}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
=\(\sqrt{9}\left(\sqrt{7}^2-\sqrt{5}^2\right)\)
=\(\sqrt{3^2}\cdot\left(7-5\right)=3\cdot2=6\)
C=\(\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}\left(\sqrt{5}-\sqrt{3}\right)\right)\)
=\(\sqrt{5}\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)\)
=\(\sqrt{5}\left(5-3\right)\)=\(2\sqrt{5}\)