Question

\(P=\frac{\sqrt{x}+1}{\sqrt{x}-1}+1\)

a) Rút gọn P

b) Tìm giá trị của P tại \(x=4-2\sqrt{3}\)

c)tìm Min P

d) tìm gt của x thỏa mãn P=2P

Answer 1

\(P=\frac{\sqrt{x}+1}{\sqrt{x}-1}+1\)

\(P=\frac{\sqrt{x}+1+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(P=\frac{2\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(P=\frac{2\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(P=\frac{2}{\sqrt{x}-1}\)

vay \(P=\frac{2}{\sqrt{x}-1}\)

b)  \(x=4-2\sqrt{3}\)

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

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

thay \(x\) vao ta co:

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

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

\(P=\sqrt{3}-1\) ( vi \(\sqrt{3}-1>0\))

vay \(P=\sqrt{3}-1\)