Question

Phân tích đa thức thành nhân tử:

\(y=7\sqrt{x-1}+x-1-\sqrt{x^3-x^2}\) với \(x\ge1\)

Answer 1

\(x+\left(7-x\right)\sqrt{x-1}-1\)

Answer 2

= căn(x-1) *(7 + căn(x-1) - x)

Answer 3

\(y=7\sqrt{x-1}+x-1-\sqrt{x^3-x^2}=7\sqrt{x-1}+x-1-x\sqrt{x-1}=\sqrt{x-1}\left(\sqrt{x-1}-x+7\right)\)

Answer 4

y=7\(\sqrt{x-1}\)+x-1-\(\sqrt{x^3-x^2}\)

y=7\(\sqrt{x-1}\)+(x-1)-\(\sqrt{x^2\left(x-1\right)}\)

y=7\(\sqrt{x-1}\)+(x-1)-\(\sqrt{x^2}\)\(\sqrt{x-1}\)

vì x lớn hơn hằng bằng 1 (gt) nên y tương đương

y=7\(\sqrt{x-1}\)+(x-1)-x\(\sqrt{x-1}\)

y=\(\sqrt{x-1}\)(7-x+\(\sqrt{x+1}\))