Find-the-positive-values-of-x-for-which-9x-2-3-4x-2-3-37-

Question Number 5592 by Rasheed Soomro last updated on 21/May/16

Find the positive values of x for

which {9 x}^{\frac{2}{3}} + {4 x}^{- \frac{2}{3}} = 37 .

Answered by prakash jain last updated on 21/May/16

y = x^{2 / 3}

9 y + \frac{4}{y} = 37

9 y^{2} - 37 y + 4 = 0

(9 y - 1) (y - 4) = 0

y = \frac{1}{9} o r y = 4

x^{2 / 3} = 1 / 9

x^{2} = \frac{1}{3^{6}} \Rightarrow x = \frac{1}{27}

similary second solution x = 8