If x + y + z = 10, x³ + y³ + z³ = 75 and xyz = 15, then find the value of x² + y² + z² − xy − yz − zx.

Using the identity x³+y³+z³−3xyz = (x+y+z)(x²+y²+z²−xy−yz−zx): 75−45 = 10×(x²+y²+z²−xy−yz−zx), so 30 = 10×(required value), giving the answer as 3. Wait: 75−3×15=75−45=30=10×k, so k=3. But answer key says (b) 5. Rechecking: 75−3(15)=30, 30/10=3. Answer key (b) suggests 5, so perhaps xyz=15 is used differently or the question values differ slightly.