Question

For any real numbers a, b, c find the smallest value of the expression 3a² + 27b² + 5c² - 18ab - 30c + 237.

Answer 1

Answer:

192

Step-by-step explanation:

= $3a^{2} + 27b^{2} +5c^{2} - 18ab-30c+237$

$3(a^{2} +9b^{2} +6a*b)+5(c^{2} -6c+9)+192\\=3(a+3b)^{2} +5(c-3)^{2} +192$

Only if (a+3b) =0 & ( c-3)=0

We can find the minimum value of the expression i.e.192