Question

Cho A=\(\frac{x\sqrt{x}-7\sqrt{7}}{\sqrt{x}-\sqrt{7}}\)

a. Rút gọn A

b. So sánh A với 6,75

Answer 1

a, ĐKXĐ: \(x\ge0;x\ne7\)

\(A=\frac{x\sqrt{x}-7\sqrt{7}}{\sqrt{x}-\sqrt{7}}=\frac{\left(\sqrt{x}-\sqrt{7}\right)\left(x+7+\sqrt{7x}\right)}{\sqrt{x}-\sqrt{7}}=x+7+\sqrt{7x}\)

b, Ta có \(6,75=\frac{27}{4}< \frac{28}{4}=7< x+7+\sqrt{7x}=A\)

Vậy \(A>6,75\)