Bài 4:
\(a,P=\dfrac{x+\sqrt{x}+3\sqrt{x}-3-6\sqrt{x}+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ P=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\\ c,P-1=\dfrac{\sqrt{x}-1-\sqrt{x}-1}{\sqrt{x}+1}=\dfrac{-2}{\sqrt{x}+1}< 0\left(-2< 0;\sqrt{x}+1>0\right)\\ \Leftrightarrow P< 1\)
Bài 5:
a, Vì \(\widehat{EKF}=\widehat{EHF}=90^0\) nên EKHF nội tiếp hay E,F,K,H cùng thuộc 1 đt
b, Vì \(\widehat{DKI}+\widehat{DHI}=90^0+90^0=180^0\) nên DKIH nội tiếp hay D,K,I,H cùng thuộc 1 đt
c, DKIH nt nên \(\widehat{FKI}=\widehat{FHD}\)
Do đó \(\Delta FKI\sim\Delta FHD\left(g.g\right)\Rightarrow\dfrac{FI}{FD}=\dfrac{FK}{FH}\Rightarrow FI\cdot FH=FD\cdot FK\)
