Question

Let f(t)=sqrt(1+t^2) - t. Find the value of the expression:
f(x)f(y)+f(y)f(z)+f(z)f(x), if xy+yz+zx =1, x, y, and z are all greater than 0.

Answer 1

all you have to do is replace the variables with the variable that is in the parenthesis, so\[f(x)=\sqrt{1+x^2-x}\]\[f(y)=\sqrt{1+y^2-y}\]\[f(z)=\sqrt{1+z^2-z}\]from there you need to FOIL the expressions together, and if you find\[xy+yz+zx\] in your result, then you replace that with 1