Question

Show x+(x-a)^2 + (x-b)^2 must equal (a+b)/2 using some value x

Calculus using IVT?

Answer 1

not sure how calculus is used here
after expanding:
\[x+(x^{2}-2ax+a^{2}) +(x^{2}-2bx +b^{2}) = \frac{a+b}{2}\]
\[2x^{2}+(1-2a-2b)x+(a^{2}+b^{2}- \frac{a+b}{2}) = 0\]
solve for x using quadratic formula