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 55887 by behi83417@gmail.com last updated on 05/Mar/19

$$a^2+1=b^2$$$$b^2+c^2=b^4$$$$ab=c$$$$\mathbf{solve}\mathbf{for}:\mathbf{a},\mathbf{b},\mathbf{c}.$$

Answered by MJS last updated on 05/Mar/19

$$b^2=a^2+1\Rightarrow {(a^2+1)}^2-(a^2+1)-c^2=0$$$$a^4+a^2-c^2=0$$$$c=ab\Rightarrow a^4+a^2-a^2(a^2+1)=0\mathrm{true}\mathrm{for}a\in \mathbb{R}$$$$\Rightarrow a\in \mathbb{R}\wedge b=\pm \sqrt{a^2+1}\wedge c=\pm a\sqrt{a^2+1}$$

Answered by JDamian last updated on 06/Mar/19

$$$$$$$$$$\mathrm{As}\mathrm{the}2\mathrm{nd}.\mathrm{and}\mathrm{the}3\mathrm{rd}.\mathrm{expressions}$$$$\mathrm{combined}\mathrm{are}\mathrm{the}\mathrm{first};\mathrm{the}\mathrm{only}\mathrm{one}\mathrm{to}\mathrm{solve}\mathrm{is}:$$$$a^2+1=b^2\Rightarrow b=\pm \sqrt{a^2+1}\Rightarrow c=\pm a\sqrt{a^2+1}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com