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 77009 by Master last updated on 02/Jan/20

Commented by Master last updated on 02/Jan/20

lose x from the system(find the connection between a and c)

$$\mathrm{lose}\:\mathrm{x}\:\mathrm{from}\:\mathrm{the}\:\mathrm{system}\left(\mathrm{find}\:\mathrm{the}\:\mathrm{connection}\:\mathrm{between}\:\mathrm{a}\:\mathrm{and}\:\mathrm{c}\right) \\ $$

Commented by MJS last updated on 02/Jan/20

solve both for c c=term_1 (a, x) c=term_2 (a, x) ⇒ term_1 (a, x) =term_2 (a, x) this leads to a polynome in x^4 &a^4 let x^4 =y∧a^4 =b we get 4 exact solutions for y but they are not “nice” and hard to handle ⇒ we can insert into c=term_1 or c=term_2 and get 4 values for c(a) but again they are not “nice”. I′m not willing to type all this, do it for yourself, the path is easy but you′ll waste plenty of paper and nerves...

$$\mathrm{solve}\:\mathrm{both}\:\mathrm{for}\:{c} \\ $$$${c}=\mathrm{term}_{\mathrm{1}} \:\left({a},\:{x}\right) \\ $$$${c}=\mathrm{term}_{\mathrm{2}} \:\left({a},\:{x}\right) \\ $$$$\Rightarrow \\ $$$$\mathrm{term}_{\mathrm{1}} \:\left({a},\:{x}\right)\:=\mathrm{term}_{\mathrm{2}} \:\left({a},\:{x}\right) \\ $$$$\mathrm{this}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{a}\:\mathrm{polynome}\:\mathrm{in}\:{x}^{\mathrm{4}} \&{a}^{\mathrm{4}} \\ $$$$\mathrm{let}\:{x}^{\mathrm{4}} ={y}\wedge{a}^{\mathrm{4}} ={b} \\ $$$$\mathrm{we}\:\mathrm{get}\:\mathrm{4}\:\mathrm{exact}\:\mathrm{solutions}\:\mathrm{for}\:{y}\:\mathrm{but}\:\mathrm{they}\:\mathrm{are} \\ $$$$\mathrm{not}\:``\mathrm{nice}''\:\mathrm{and}\:\mathrm{hard}\:\mathrm{to}\:\mathrm{handle} \\ $$$$\Rightarrow \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{insert}\:\mathrm{into}\:{c}=\mathrm{term}_{\mathrm{1}} \:\mathrm{or}\:{c}=\mathrm{term}_{\mathrm{2}} \:\mathrm{and} \\ $$$$\mathrm{get}\:\mathrm{4}\:\mathrm{values}\:\mathrm{for}\:{c}\left({a}\right)\:\mathrm{but}\:\mathrm{again}\:\mathrm{they}\:\mathrm{are}\:\mathrm{not} \\ $$$$``\mathrm{nice}''. \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{willing}\:\mathrm{to}\:\mathrm{type}\:\mathrm{all}\:\mathrm{this},\:\mathrm{do}\:\mathrm{it}\:\mathrm{for} \\ $$$$\mathrm{yourself},\:\mathrm{the}\:\mathrm{path}\:\mathrm{is}\:\mathrm{easy}\:\mathrm{but}\:\mathrm{you}'\mathrm{ll}\:\mathrm{waste} \\ $$$$\mathrm{plenty}\:\mathrm{of}\:\mathrm{paper}\:\mathrm{and}\:\mathrm{nerves}... \\ $$

Commented by Master last updated on 02/Jan/20

prove that

$$\mathrm{prove}\:\mathrm{that} \\ $$

Commented by MJS last updated on 02/Jan/20

prove that for yourself

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{yourself} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com