Question

Cho S=\(\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}=a+b\sqrt{3}\) trong đó a, b là các số nguyên . Tính tổng
T=a+b

Answer 1

Ta có: \(a+b\sqrt{3}=\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)

\(\Leftrightarrow a+b\sqrt{3}=2-\sqrt{3}-2-\sqrt{3}\)

\(\Leftrightarrow a+b\sqrt{3}=-2\sqrt{3}\)

\(\Leftrightarrow a=0;b=-2\)

T=a+b=0+(-2)=-2

Answer 2

\(S=\sqrt{\left(\sqrt{3}\right)^2-2\cdot2\sqrt{3}+2^2}-\sqrt{\left(\sqrt{3}\right)^2+2\cdot2\cdot\sqrt{3}+2^2}\)

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

\(S=\left|\sqrt{3}-2\right|-\left|\sqrt{3}+2\right|=-\sqrt{3}+2-\sqrt{3}-2=0+\left(-2\right)\sqrt{3}\)

\(a=0,b=-2\)

\(T=0+-2=-2\)