have := Real.geom_mean_le_arith_mean2_weighted hw hw ha hb (by norm_num)
a b : ℝ
ha : 0 ≤ a
hb : 0 ≤ b
hw : 0 ≤ 1 / 2
⊢ 2 * (a ^ (1 / 2) * b ^ (1 / 2)) ≤ a + b
a b : ℝ
ha : 0 ≤ a
hb : 0 ≤ b
hw : 0 ≤ 1 / 2
this : a ^ (1 / 2) * b ^ (1 / 2) ≤ 1 / 2 * a + 1 / 2 * b
⊢ 2 * (a ^ (1 / 2) * b ^ (1 / 2)) ≤ a + b