Question

show that the function f(x)=(x-a)^2*(x-b)^2+1 has a solution of (a+b)/2 for some value of x.

Answer 1

are you supposed to show this using any particular method ?

Answer 2

No.

Answer 3

you should be able to set that expression equal to (a+b)/2, then solve for x. if you can determine x in terms of a and b, you will be finished.

Answer 4

\[(x - a)^2 * (x - b)^2 + 1 = \frac{ a + b }{ 2 }\]
\[(( x - a)(x - b))^2 = \frac{ a + b }{ 2 } - 1\]
\[(x - a)(x - b) = \sqrt{\frac{ a + b }{ 2 } - 1}\]
\[x^2 -ax - bx + ab = . . . etc.\]