Question
Let a,b be real numbers, such that ab-4a+4b=18. Find the minimum value of a^2+b^2
Let a,b be real numbers, such that ab-4a+4b=18. Find the minimum value of a^2+b^2
Let
Taking square of equation (1) gives
Substitute (2) and solve for ab
Substitute (4) and(1) to given equation ab-4a+4b=18, then
Rearrange terms to the form of a quadratic function.
Therefore, the minimum value of y, that is, a^2+b^2 is 20 when x= -4