Question

ai giúp mình với mình cần gấp, tối nay là mk phải nộp rồi:

a) rút gọn P

\(\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{\sqrt{x}+1}{\sqrt{x}-1}\right).\left(\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}\right)^2\)

b) tính P tại x= \(3-2\sqrt{2}\)

c) tìm x để P>0

Answer 1

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

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

thay vao biểu thức

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

Answer 2

(\(\frac{\sqrt{X}-1}{\sqrt{x}+1}\)-\(\frac{\sqrt{x}+1}{\sqrt{x}-1}\))*(\(\frac{1}{2\sqrt{x}}\)-\(\frac{\sqrt{x}}{2}\))^2

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

=(\(\frac{-4\sqrt{x}}{x-1}\))*(\(\frac{\left(x-1\right)^2}{4x}\)

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