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\(\frac{x+2+\sqrt{x^2-4}}{x+2-\sqrt{x^2-4}}+\frac{x+2-\sqrt{x^2-4}}{x+2+\sqrt{x^2-4}}\)
\(=\frac{\left(x+2+\sqrt{x^2-4}\right)^2+\left(x+2-\sqrt{x^2-4}\right)^2}{\left(x+2+\sqrt{x^2-4}\right)\left(x+2-\sqrt{x^2-4}\right)}\)
\(=\frac{\left(x^2+4+x^2-4+4x+2\sqrt{x^2-4}+x\sqrt{x^2-4}\right)+\left(x^2+4+x^2-4+4x-2\sqrt{x^2-4}-x\sqrt{x^2-4}\right)}{x^2+2x-x\sqrt{x^2-4}+2x+4-2\sqrt{x^2-4}+x\sqrt{x^2-4}+2\sqrt{x^2-4}-x^2+4}\)\(=\frac{4x^2+8x}{4x+8}=\frac{4x\left(x+2\right)}{4\left(x+2\right)}=x\)
\(DK:x\ne1,-1,-2\)
\(\frac{x+2+\sqrt{x^2-4}}{x+2-\sqrt{x^2-4}}+\frac{x+2-\sqrt{x^2-4}}{x+2+\sqrt{x^2-4}}\)
\(=\frac{\left(x+2+\sqrt{x^2-4}\right)^2+\left(x+2-\sqrt{x^2-4}\right)}{\left(x+2\right)^2-x^2+4}\)
\(=\frac{\left(x+2\right)^2+2\left(x+2\right)\sqrt{x^2-4}+x^2-4+\left(x+2\right)^2-2\left(x+2\right)\sqrt{x^2-4}+x^2-4}{4x+8}\)
\(=\frac{4x^2+8x-8}{4x+8}\)
\(=\frac{x^2+2x-2}{x+2}\)
(14,78-a)/(2,87+a)=4/1
14,78+2,87=17,65
Tổng số phần bằng nhau là 4+1=5
Mỗi phần có giá trị bằng 17,65/5=3,53
=>2,87+a=3,53
=>a=0,66.
a,\(\sqrt{x-4+4\sqrt{x-4}+4}\) +\(\sqrt{x-4-4\sqrt{x-4}+4}\)
=\(\sqrt{x-4}+2+\left|\sqrt{x-4}-2\right|\) (vi x>=8)
=\(\sqrt{x-4}+2+\sqrt{x-4}-2=2\sqrt{x-4}\)
b, \(\sqrt{x-1+2\sqrt{x\left(x-1\right)}+x}+\sqrt{x-1-2\sqrt{x\left(x-1\right)}+x}\)
=\(\sqrt{x-1}+\sqrt{x}+\left|\sqrt{x-1}-\sqrt{x}\right|\)
=\(\sqrt{x}+\sqrt{x-1}+\sqrt{x}-\sqrt{x-1}\) =\(2\sqrt{x}\)
c,d sai dau bai hay sao y
\(\frac{x+2+\sqrt{x^2-4}}{x+2-\sqrt{x^2-4}}+\frac{x+2-\sqrt{x^2-4}}{x+2+\sqrt{x^2-4}}\)
\(=\frac{\left(\sqrt{x+2}\right)^2+\sqrt{x-2}\cdot\sqrt{x+2}}{\left(\sqrt{x+2}\right)^2-\sqrt{x-2}\cdot\sqrt{x+2}}+\frac{\left(\sqrt{x+2}\right)^2-\sqrt{x-2}\cdot\sqrt{x+2}}{\left(\sqrt{x+2}\right)^2+\sqrt{x-2}\cdot\sqrt{x+2}}\)
\(=\frac{\sqrt{x+2}\left(\sqrt{x+2}+\sqrt{x-2}\right)}{\sqrt{x+2}\left(\sqrt{x+2}-\sqrt{x-2}\right)}+\frac{\sqrt{x+2}\left(\sqrt{x+2}-\sqrt{x-2}\right)}{\sqrt{x+2}\left(\sqrt{x+2}+\sqrt{x-2}\right)}\)
\(=\frac{\sqrt{x+2}+\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-2}}+\frac{\sqrt{x+2}-\sqrt{x-2}}{\sqrt{x+2}+\sqrt{x-2}}\)
\(=\frac{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2+\left(\sqrt{x+2}-\sqrt{x-2}\right)^2}{\left(\sqrt{x+2}-\sqrt{x-2}\right)\left(\sqrt{x+2}+\sqrt{x-2}\right)}\)
\(=\frac{x+2+x-2+2\sqrt{\left(x+2\right)\left(x-2\right)}+x+2+x-2-2\sqrt{\left(x+2\right)\left(x-2\right)}}{x+2-x+2}\)
\(=\frac{4x}{4}\)
\(=x\)