VTMO 2026 - Grade 7 - Final - SET 4 - Self-study Question 2

a) Prove that if $\frac ab=\frac cd$, then $\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}$.

b) Find the minimum value of $C=\frac6{|x|-3}$ for integer $x$.