IF X2+ Y2=9 AND 4a2+ 9b2 =16 then the minimum value of 4a2x2 + 9b2y2 -12axyb is - Maths - Limits and Derivatives

Question

IF X2 + Y2 =9 AND 4a2 +
9b2 =16 then the minimum value of
4a2x2 + 9b2y2 -12axyb
is

Rahul Raj · Accepted Answer

dear student

AM≥GMso, x2+y22≥x2y2=xy or xy≤9/2and 4a2+9b22≥4a29b2=6ab or 6ab≤16/2 or ab≤4/3combining bothaxby≤6given expression = 4a2x2+9b2y2-12axyb=4a2x2+9b2y2+12axyb-24axyb=(2ax+3by)2-24axybnow least value of2ax+3byis when2ax+3by2≥2ax×3by=6axby=6×6=62ax+3by≥12least value of expression=122-24×6=144-144=0

regards

IF X2 + Y2 =9 AND 4a2 + 9b2 =16 then the minimum value of 4a2x2 + 9b2y2 -12axyb is

IF X² + Y² =9 AND 4a² + 9b² =16 then the minimum value of 4a²x²+ 9b²y² -12axyb is