Question

solve x^2+(ax/a+x)^2=3a^2

Answer 1

x^2 + (ax / (a + x) )^2 = 3 a^2 if x != -a
x^2 + a^2 . x^2 / (a + x)^2 = 3 . a^2
NOTE:
(A + B)^2 = A^2 + B^2 + 2 . A . B
continue with the answer
x^2 . (a^2 + x^2 + 2 . a . x) + a^2 . x^2 / (a^2 + x^2 + 2 . a . x) = 3 . a^2
(x^4 + 2 . a^2 . x^2 + 2 . a . x^3) / (a^2 + x^2 + 2ax) - 3 . a^2 = 0
(x^2 . (x^2 + 2 . a . x +2 . a^2) . (3 . a^2 . (x + a)^2) ) / (1 . (x + a)^2) = 0
(x^4  + 2 . x^3 . a - x^2 . a^2 - 6 . x . a^3 - 3a^4) / (x + a)^2 = 0
( (x^4 + 2 . x^3 . a - x^2 . a^2 - 6 . x . a^3 - 3a^4 ) / (x + a)^2) . (x + a)^2 = 0 . (x + a)^2
now eq. takes the shapes:-
x^4 + 2 . x^3 . a - x^2 . a^2 - 6 . x . a^3 - 3 . a^4=0
we will noth handles this type of equation at this time.