#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# a+b+c = 3,then find the greatest value of a^2b^3c^2. Nishant Vora IIT Patna
6 years ago
Hello Student, Please find the solution

Given a+b+c =3
Write this as

Now we will use AM >= GM

So

Therefore,

So greatest value of is

10 months ago

iven: 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