if a/2 = b/3=c/4 then,find the value of (a+b+c)/2b if a/2 = b/3=c/4 then,find the value of (a+b+c)/2b
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Answer:
Given: a + 2b + 3c = 4
=> a = 4- 2b - 3c
To find : Minimum value of a² + b² + c² OR to find min value of (4–2b - 3c)² + b² + c² , here we have 2 variables related by the above shown expression. Let's suppose its minimum value is ‘m'
m = (4–2b-3c)² + b² + c² . . . . . . . . . . . (1)
The derivative of m wrt b = Polynomial can be differentiated by power rule (d/dx) x^n = n x^(n-1)
dm/ db = (-2) (2) ( 4–2b - 3c)^(2–1) + 2b=0 ( by quotient rule)
=> -16 + 8b +12c + 2b = 0
=> 10b + 12c = 16
=> 5b + 6c = 8 . . . . . . . . . (2)
Next, the derivative of m wrt c =
dm/dc = (-3) (2) ( 4–2b - 3c)^(2–1) + 2c =0
=> -24 + +12b +18c + 2c = 0
=> 12b + 20c = 24
=> 3b + 5c = 6 . . . . . . . . . . . .(3)
By solving eq (1) & eq(2)
We get b= 4/7 , c = 6/7
Since, ‘m’ is the minimum value of the expression
So, we substitute the values of b & c in eq (2) & (3), to get the value of m.
(4 - 2*4/7 - 3*6/7 )² + (4/7)² + (6/7)²
= ( 4- 8/7 - 18/7)² + 16/49 + 36/49
= 4/49 + 16/49 + 36/49
= 56/49
= 8/7
Step-by-step explanation:
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