求解 根號 1.若a+b=12,ab=9,求b/a^(1/2)+a/b^(1/2)的值?

解法一:
√(b/a) + √(a/b)
= √b / √a + √a / √b
= √b√b / (√a√b) + √a√a / (√a√b)
= b / √(ab) + a / √(ab)
= (a + b) / √(ab)
= 12 / √9
= 4

解法二:
√(b/a) + √(a/b) 全式平方
= b/a + 2√(b/a) √(a/b) + a/b
= b/a + 2 + a/b
= (a² + 2ab + b²) / (ab)
= (a + b)² / (ab)
= 12² / 9
= 16
∴ √(b/a) + √(a/b) = √16 = 4

(b/a)^1/2 +(a/b)^1/2
=(b+a)/[(ab)^0.5]
=12/(9^0.5)
=4