Question

已知a,b属于R+和x,y属于R+，满足a+b=13,a/x+b/y=1,若x+y的最小值为25，求a，b的值

Answer 1

你好！

x+y
= (x+y)(a/x + b/颤腊y) 【因为a/x+b/y=1】
= a+b + ay/段洞稿握孝x + bx/y
= 13 + ay/x + bx/y
≥ 13 + 2√ (ay/x * bx/y)
= 13 + 2√(ab)
= 25
解得 ab = 36
联立a+b=13
解得 a=4,b=9或a=9,b=4

Answer 2

x+y
= (x+y)(a/x + b/y) 【因为a/燃歼x+b/世戚y=1】
= a+b + ay/x + bx/y
= 13 + ay/x + bx/y
≥ 13 + 2√ (ay/x * bx/y)
= 13 + 2√(ab)
= 25
解得 ab = 36
联立皮返冲a+b=13
解得 a=4,b=9或a=9,b=4