8-x-2-4-2x-3-1-x-1-2-5x-5-1-6-

Question Number 53935 by Mikael_Marshall last updated on 27/Jan/19

\sqrt{8^{x - 2}} \times \sqrt[x + 1]{4^{2 x - 3}} = \sqrt[6]{2^{5 x + 5}}

Answered by Kunal12588 last updated on 27/Jan/19

2^{\frac{3 x - 6}{2}} \times 2^{\frac{4 x - 6}{x + 1}} = 2^{\frac{5 x + 5}{6}}

\Rightarrow \frac{3 x - 6}{2} + \frac{4 x - 6}{x + 1} = \frac{5 x + 5}{6}

\Rightarrow \frac{4 x - 6}{x + 1} = \frac{5 x + 5}{6} - \frac{9 x - 18}{2} = \frac{5 x + 5 - 9 x + 18}{2}

\Rightarrow \frac{4 x - 6}{x + 1} = \frac{23 - 4 x}{6}

\Rightarrow 24 x - 36 = 23 x - 4 x^{2} + 23 - 4 x

\Rightarrow 4 x^{2} + 5 x - 59 = 0

c o m p a r i n g w i t h s t d . f o r m o f q u a d . {e q}^{n} .

a = 4, b = 5, c = - 59

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{- 5 \pm \sqrt{25 + 944}}{8}

x = \frac{\pm \sqrt{969} - 5}{8} = \frac{\pm \sqrt{3} \sqrt{17} \sqrt{19} - 5}{8} (u s e c a l c u l a t o r)

Commented by Kunal12588 last updated on 27/Jan/19

3.2660956 and −4.5160956 from calculator