Question 4
Let $x,y,z$ be real numbers less than $4$. Prove that among $$\frac1x+\frac1{4-y},\qquad\frac1y+\frac1{4-z},\qquad\frac1z+\frac1{4-x}$$ there is at least one number greater than or equal to $1$.
The printed assumptions contain a domain/validity defect. Retain those assumptions and assess whether the requested claim follows; identify undefined cases or counterexamples if necessary. Any additional condition must be stated as a correction, not as an original given.
The printed assumptions contain a domain/validity defect. Retain those assumptions and assess whether the requested claim follows; identify undefined cases or counterexamples if necessary. Any additional condition must be stated as a correction, not as an original given.