Question

[Trần Nguyên Sơn]

1. P=\(\left(1+\frac{a+\sqrt{a}}{\sqrt{a}+1}\right)\times\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)

a. Rút gọn P.

b. Tìm a biết \(P=\sqrt{a}\)

Answer 1

[Lê Nguyễn Huyền Anh]

a,\(P=1-\left(\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)^2=1-\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a-1}}\right)^2=1-a\)(đk : tự tìm nhé )

b, \(1-a=\sqrt{a}< =>a+\sqrt{a}-1=0\)

\(< =>4a+4\sqrt{a}+1-5=0\)

\(< =>\left(2\sqrt{a}+1\right)^2-\sqrt{5}^2=0\)

\(< =>\left(2\sqrt{a}+1-\sqrt{5}\right)\left(2\sqrt{a}+1+\sqrt{5}\right)=0\)

<=> ...

Answer 2

[Lê Nguyễn Huyền Anh]

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

\(=1-\sqrt{a}+\sqrt{a}-\frac{\sqrt{a}.\left(\sqrt{a}+1\right).\sqrt{a}.\left(\sqrt{a}-1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}=1-a\)

câu b thì giống câu lúc nãy mình làm