solve-for-x-in-terms-of-a-R-x-x-x-2-a-x-a-2-a-2-

Question Number 73131 by behi83417@gmail.com last updated on 06/Nov/19

solve for x, in terms of : a \in R .

x + \sqrt{x} + \sqrt{x^{2} - a} + \sqrt{x - a^{2}} = a^{2}

Commented by mr W last updated on 06/Nov/19

x ⩾ 0

x - a^{2} ⩾ 0

x^{2} - a ⩾ 0

(x - a^{2}) + \sqrt{x} + \sqrt{x^{2} - a} + \sqrt{x - a^{2}} ⩾ 0

\Rightarrow o n l y s o l u t i o n i s, w h e n

x - a^{2} = 0

x = 0

x^{2} - a = 0

\Rightarrow a = 0 a n d x = 0

i f a \neq 0, t h e r e i s n o s o l u t i o n .

Commented by behi83417@gmail.com last updated on 06/Nov/19

thanks in advance dear master .