Question

雲朵泡泡

求解🙏

7.已知a,b,c,dER/a²+b²+c²+d²+7≤2a-4b-2c+2d,若a+b+c-d之值為何?
[-1]

Answer 1

qn

a²-2a + b²+4b + c²+2c +d²-2d + 7 ≤ 0
(a²-2a+1) + (b²+4b+4) + (c²+2c+1) + (d²-2d+1) ≤ 0
(a-1)² + (b+2)² + (c+1)² + (d-1)² ≤ 0

由於 (a-1)² + (b+2)² + (c+1)² + (d-1)² ≥ 0
(等號成立條件 a-1 = b+2 = c+1 = d-1 = 0)
故 a=1 , b=-2 , c=-1 , d=1