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 158185 by HongKing last updated on 31/Oct/21

Commented by MJS_new last updated on 31/Oct/21

obviously x=1 is a solution

$$\mathrm{obviously}\:{x}=\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution} \\ $$

Commented by HongKing last updated on 31/Oct/21

how dear Ser, please, thank you

$$\mathrm{how}\:\mathrm{dear}\:\boldsymbol{\mathrm{S}}\mathrm{er},\:\mathrm{please},\:\mathrm{thank}\:\mathrm{you} \\ $$

Commented by MJS_new last updated on 31/Oct/21

with x=1 we have  x^3 =1  ((x−1)/(x^3 +1))=(0/2)=0  ((x^3 (x+1))/(x^4 +1))=(2/2)=1  (((x−1)(x^2 +1))/x^4 )=(0/1)=0  ⇒  1+0=1+0 true

$$\mathrm{with}\:{x}=\mathrm{1}\:\mathrm{we}\:\mathrm{have} \\ $$$${x}^{\mathrm{3}} =\mathrm{1} \\ $$$$\frac{{x}−\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{1}}=\frac{\mathrm{0}}{\mathrm{2}}=\mathrm{0} \\ $$$$\frac{{x}^{\mathrm{3}} \left({x}+\mathrm{1}\right)}{{x}^{\mathrm{4}} +\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1} \\ $$$$\frac{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{4}} }=\frac{\mathrm{0}}{\mathrm{1}}=\mathrm{0} \\ $$$$\Rightarrow \\ $$$$\mathrm{1}+\mathrm{0}=\mathrm{1}+\mathrm{0}\:{true} \\ $$

Commented by HongKing last updated on 01/Nov/21

thank you very much dear Ser cool

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{dear}\:\boldsymbol{\mathrm{S}}\mathrm{er}\:\mathrm{cool} \\ $$

Commented by MJS_new last updated on 01/Nov/21

there might be other solutions but this turns  into a polynome of 12^(th)  degree...

$$\mathrm{there}\:\mathrm{might}\:\mathrm{be}\:\mathrm{other}\:\mathrm{solutions}\:\mathrm{but}\:\mathrm{this}\:\mathrm{turns} \\ $$$$\mathrm{into}\:\mathrm{a}\:\mathrm{polynome}\:\mathrm{of}\:\mathrm{12}^{\mathrm{th}} \:\mathrm{degree}... \\ $$

Commented by HongKing last updated on 01/Nov/21

yes thank you my dear Ser

$$\mathrm{yes}\:\mathrm{thank}\:\mathrm{you}\:\mathrm{my}\:\mathrm{dear}\:\boldsymbol{\mathrm{S}}\mathrm{er} \\ $$

Commented by MJS_new last updated on 01/Nov/21

I found 2 more real solutions  x≈−1.41949255805  x≈−.864853259707  and 10 complex solutions exist

$$\mathrm{I}\:\mathrm{found}\:\mathrm{2}\:\mathrm{more}\:\mathrm{real}\:\mathrm{solutions} \\ $$$${x}\approx−\mathrm{1}.\mathrm{41949255805} \\ $$$${x}\approx−.\mathrm{864853259707} \\ $$$$\mathrm{and}\:\mathrm{10}\:\mathrm{complex}\:\mathrm{solutions}\:\mathrm{exist} \\ $$

Commented by HongKing last updated on 01/Nov/21

Thank you so much my dear Ser

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much}\:\mathrm{my}\:\mathrm{dear}\:\boldsymbol{\mathrm{Ser}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com