Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 116192 by bemath last updated on 01/Oct/20

Commented by MJS_new last updated on 01/Oct/20

$$x=y=z=0$$$$\mathrm{not}\mathrm{sure}\mathrm{how}\mathrm{to}\mathrm{further}\mathrm{solve}\mathrm{it}$$

Answered by TANMAY PANACEA last updated on 01/Oct/20

$$(1+xy)(\frac{1}{x}+\frac{1}{y})=5$$$$\frac{1}{x}+\frac{1}{y}+x+y=5$$$$\frac{1}{y}+\frac{1}{z}+y+z=6$$$$\frac{1}{z}+\frac{1}{x}+z+x=7$$$$x+y+z+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{18}{2}=9$$$$z+\frac{1}{z}=4\to z^2-4z+1=0$$$$z=\frac{4\pm \sqrt{16-4}}{2}=\frac{4\pm 2\sqrt{3}}{2}=2\pm \sqrt{3}$$$$y+\frac{1}{y}=2\to {(y-1)}^2=0\to y=1,1$$$$x+\frac{1}{x}=3\to x^2-3x+1=0$$$$x=\frac{3\pm \sqrt{9-4}}{2}=\frac{3\pm \sqrt{5}}{2}$$

Commented by MJS_new last updated on 01/Oct/20

$$\mathrm{great}!$$

Commented by TANMAY PANACEA last updated on 01/Oct/20

$$thankyousir$$

Answered by bobhans last updated on 02/Oct/20

Terms of Service

Privacy Policy

Contact: info@tinkutara.com