Only Genius Can Solved | Algebra Math Olympiad Problems | Find the Value of a = ? and b = ?

[@اسماعیلخسروی-خ6ظ]

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[@RealQinnMalloryu4]

(b ➖ 2a+1) (a ➖ 2b+1).

[@Swarit_y7hs]

Question Source???

[@rafaelfelipe4753]

Incomplete solution. (3+√5)/2 also solve

[@SidneiMV]

1 + √(1/a) = 1/b
1 + √(1/b) = 1/a
√(1/a) = u
√(1/b) = v
1 + u = v²
1 + v = u²
u² - v² = -(u -v)
(u - v)(u + v + 1) = 0
v = u ∨ v = -(u + 1)
v = u
1 + v = u²
u² - u - 1 = 0
u = (1 ± √5)/2
√(1/a) = (1 + √5)/2
1/a = (3 + √5)/2
a = (3 - √5)/2 => b = (3 - √5)/2