Question

For any real number a,b,c find the smallest value of the expression 3a^2+27b^2+5c^2-18ab-30c+237.

Answer 1

Answer:

Step-by-step explanation:

3a^2+27b^2+5c^2-18ab-30c+237

3a^2+27b^2-18ab = (√3a - 3√3b)²

there fore minimum value of above expression is zero

now, the remaining equation is

5c^2-30c+237

so differentiate wrt c and equate it to zero to find the max or min value of this exp..

10c-30=0

c=3

hence minimum value of 3a^2+27b^2+5c^2-18ab-30c+237 is

(√3a - 3√3b)² +  5c^2-30c+237

0 + 5×3² - 30×3 +237 = 192