Q5 - Completing the square with multiple quadratic terms
Question 5: $$ \text{If } a^2 + 5b^2 + 4c^2 - 4ab - 4bc = 0 \text{ then find the value of } \frac{a^2 + ac}{b^2}. $$ Solution: 1. First we will complete the square in "a" since a^2 has the coefficient of 1. So we get: \((a -2b)^2 + ... = 0\) 2. Now we complete the square of the remaining terms to get: \((a - 2b)^2 + (b - 2c)^2 = 0.\) If two squares add up to 0 then they are individually 0. So a = 2b and b = 2c. Put the value of a,c in terms of b in the question to get the answer which is 5.