Math Question and Answers


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 146244 by mathdanisur last updated on 12/Jul/21

${(\sqrt{5} - 2)}^{\frac{2 x^{2} - 1}{2}} = {(\sqrt{5} + 2)}^{\frac{3 x - 7}{4}} \Rightarrow x = ?$
	Answered by gsk2684 last updated on 12/Jul/21

	$u s e \sqrt{5} - 2 = \frac{1}{\sqrt{5} + 2}$ $c o m p a r e e x p o n e n t s$
	Answered by Olaf_Thorendsen last updated on 12/Jul/21

	${(\sqrt{5} - 2)}^{\frac{2 x^{2} - 1}{2}} = {(\sqrt{5} + 2)}^{\frac{3 x - 7}{4}}$ $\frac{2 x^{2} - 1}{2} \ln (\sqrt{5} - 1) = \frac{3 x - 7}{4} \ln (\sqrt{5} + 2)$ $2 (2 x^{2} - 1) \ln (\sqrt{5} - 1) = - (3 x - 7) \ln (\sqrt{5} - 2)$ $2 (2 x^{2} - 1) + (3 x - 7) = 0$ $4 x^{2} + 3 x - 9 = 0$ $x = \frac{- 3 \pm \sqrt{9 - 4 \times 4 \times (- 9)}}{8}$ $x = \frac{- 3 \pm 3 \sqrt{17}}{8} = - \frac{3}{8} (1 \mp \sqrt{17})$
	Commented by mathdanisur last updated on 12/Jul/21

	$t h a n k y o u S e r$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum