the minimum value of the expression (3b+4c)/a + (4c+a)/3b + (a+3b)/4c
Answers
minimum value of (3b+4c)/a + (4c+a)/3b + (a+3b)/4c = 6
Step-by-step explanation:
assuming a , b & c are positive
(3b+4c)/a + (4c+a)/3b + (a+3b)/4c
= {12bc(3b + 4c) + 4ac(4c + a) + 3ab(a + 3b) } / 12abc
= (36b²c + 48bc² + 16ac² + 4a²c + 3a²b + 9ab² ) / 12abc
= ( 4c(a² + 9b²) + 3b(a² + 16c²) + a(9b² + 16c²) ) / 12abc
= ( 4c ((a - 3b)² + 6ab ) + 3b( (a - 4c)² + 8ac) + a( (3b - 4c)² + 24bc) ) /12abc
= (4c (a - 3b)² + 3b (a - 4c)² + a (3b - 4c)² + 24abc + 24abc + 24abc )/12abc
minumum value of (a - 3b)² = 0 (a - 4c)² = 0 (3b - 4c)² = 0
= 72abc/12abc
= 6
minimum value of (3b+4c)/a + (4c+a)/3b + (a+3b)/4c = 6
if a , b , c are not necessarily positive
then ( 4c ((a + 3b)² - 6ab ) + 3b( (a + 4c)² - 8ac) + a( (3b + 4c)² - 24bc) ) /12abc
= - 72abc/12abc
= - 6
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If 9a^2+ 16b^2 +c^2 +25 =24{a+b} then value of 3a+4b+5c in numeric value is
https://brainly.in/question/12833474
https://brainly.in/question/12371255
Answer:
answer is 6
pls mark as brainiest
Step-by-step explanation: