If-x-7-x-50-Find-the-value-of-the-expression-x-1-x-

Question Number 154973 by mathdanisur last updated on 23/Sep/21

If x + \frac{7}{\sqrt{x}} = 50

Find the value of the expression

\sqrt{x} - \frac{1}{\sqrt{x}} = ?

Answered by mr W last updated on 23/Sep/21

l e t t = \sqrt{x} > 0

t^{3} - 50 t + 7 = 0

(t - 7) (t^{2} + 7 t - 1) = 0

\Rightarrow t = 7 ✓

\Rightarrow t = \frac{- 7 + \sqrt{53}}{2} ✓

\Rightarrow t = \frac{- 7 - \sqrt{53}}{2} (r e j e c t e d)

\sqrt{x} - \frac{1}{\sqrt{x}} = t - \frac{1}{t} = 7 - \frac{1}{7} = \frac{48}{7} o r

\sqrt{x} - \frac{1}{\sqrt{x}} = \frac{- 7 + \sqrt{53}}{2} - \frac{2}{- 7 + \sqrt{53}} = - 7

Commented by mathdanisur last updated on 23/Sep/21

Very nice solution, S er thankyou