Can you solve this and explain it?

Question

if o <= x <= y and (x + y)^2 - (x-y)^2 >= 25
what is the least possible value of y ?

Answer 1

(x+y)² - (x-y)² ≥ 25
x² + 2xy + y² - x² + 2xy - y² ≥ 25
4xy ≥ 25
y ≥ 25/(4x)
for x ≥ 0, that's the right half of a hyperbola, shaded above.
for y ≥ x ≥ 0, that's the line y = x, shaded above.
so the minimum y is the bottom of the overlapping region where y = x intersects with y = 25/(4x), so we solve
y = 25/(4y)
y² = 25/4
y = 5/2

Answer 2

(x + y)^2 - (x-y)^2 >= 25
(x+y - x+y)(x+y + x-y) = 2y *2x >= 25
x= y=3