a-a-x-a-a-x-2x-this-is-the-solution-Sir-Aifour-and-me-found-trivial-solution-a-x-0-a-x-R-x-2-8-r-r-2-4-2-4a-1-r-2-r-r-2-4-with-r-2-4a-3-3-sin-1-

Question Number 61490 by MJS last updated on 03/Jun/19

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

this is the solution Sir Aifour and me found

trivial solution a = x = 0

a, x \in R

x = \frac{\sqrt{2}}{8} (r + \sqrt{r^{2} + 4}) \sqrt{2 (4 a - 1) - r^{2} - r \sqrt{r^{2} + 4}}

with

r = - 2 \sqrt{\frac{4 a - 3}{3}} \sin (\frac{1}{3} \arcsin \frac{3 \sqrt{3}}{{(4 a - 3)}^{\frac{3}{2}}})

no solution for a < a_{0} with a_{0} \approx 1.509830340886

Commented by MJS last updated on 03/Jun/19

Commented by maxmathsup by imad last updated on 03/Jun/19

t h a n k s s i r m j s a n d s i r a j f o u r \dots

Commented by MJS last updated on 03/Jun/19

The path had been found by Sir Aifour, I added some odds and ends. So it's an Indian-Austrian team work ��

Commented by behi83417@gmail.com last updated on 03/Jun/19

great job done by : MJS & Ajfour .

congratulation to you two and forum!

Commented by Rasheed.Sindhi last updated on 08/Jun/19

{\frac{A}{M} \overset{⧫}{J} \frac{S}{4}}

Commented by ajfour last updated on 03/Jun/19

T h a n k s E v e r y o n e & d e a r M j S S i r .

Commented by Tawa1 last updated on 03/Jun/19

Wow, that is great sirs

Commented by mr W last updated on 03/Jun/19

w o w! f a n t a s t i c!

Commented by ajfour last updated on 04/Jun/19

Commented by ajfour last updated on 04/Jun/19

A r e p r e s e n t a t i o n (g e o m e t r i c) .

Facebook Tweet Pin