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 99796 by harckinwunmy last updated on 23/Jun/20

Answered by 1549442205 last updated on 30/Jun/20

$$\mathrm{Our}\mathrm{problem}\mathrm{is}\mathrm{equivalent}\mathrm{to}\mathrm{solve}\mathrm{the}$$$$\mathrm{system}\mathrm{of}\mathrm{the}\mathrm{equations}:\{\begin{array}{l}{\mathrm{y}}^2=4^{\mathrm{x}}\left(1\right)\\ {\mathrm{y}}^{\mathrm{x}}=16\left(2\right)\end{array}(\ast )$$$$\left(1\right)\iff {\mathrm{y}}^2={\left(2^{\mathrm{x}}\right)}^2\iff \mathrm{y}=2^{\mathrm{x}}.\mathrm{Putting}\mathrm{this}\mathrm{into}$$$$\left(2\right)\mathrm{we}\mathrm{get}{\left(2^{\mathrm{x}}\right)}^{\mathrm{x}}=2^4\iff 2^{{\mathrm{x}}^2}=2^4\iff {\mathrm{x}}^2=4$$$$\iff \mathrm{x}=\pm 2,\mathrm{y}=\in \{4;\frac{1}{4}\}\Rightarrow (\mathrm{x};\mathrm{y})\in \{(2;4);(-2;\frac{1}{4})\}\mathrm{is}\mathrm{root}\mathrm{of}\mathrm{the}$$$$\mathrm{system}(\ast ).\mathbf{Hence},\mathbf{A}\cap \mathbf{B}=\{(2;4);(-2;\frac{1}{4})\}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com