Question

1. Rút gọn : \(\sqrt{24+8\sqrt{15}-\sqrt{9-4\sqrt{5}}}\)

2. Cho: A = \(\sqrt{\frac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)

a) Rút gọn A

b) Tìm số nguyên x để A là số nguyên

 

Answer 1

Bài 1:

\(\sqrt{24+8\sqrt{15}-\sqrt{9-4\sqrt{5}}}\)

\(=\sqrt{24+8\sqrt{15}-\left(\sqrt{5}-2\right)}\)

\(=\sqrt{26+8\sqrt{15}-\sqrt{5}}\)

Bài 2:

\(A=\sqrt{\frac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)

\(A=\sqrt{\frac{x^4+6x^2+9}{x^2}}\)

\(A=\frac{\sqrt{x^4+6x^2+9}}{\sqrt{x^2}}\)

\(A=\frac{\sqrt{\left(x^2+3\right)^2}}{x}\)

\(A=\frac{x^2+3}{x}\)

\(A=\frac{x^2+3}{x}+x-2\)

\(A=\frac{2x^2+3}{x}-2\)

Answer 2

wrecking ball sai rồi \(\frac{\sqrt{\left(x^2+3\right)^2}}{x}=\frac{trituyetdoix^2+3}{x}\) bằng