Question

if a² + b² + c² -ab-bc-ca=0, prove that a=b=c

Answer 1

if a=b=c then   a²+b²+c²-a×a-b×b-c×c=0

a²+b²+c²-a²-b²-c²=0

0=0 so a=b=c

Answer 2

Step-by-step explanation:

We have,

a² + b² + c² - ab - bc - ca = 0

=> 2a² + 2b² + 2c² - 2ab - 2bc - 2ca = 2 × 0

=> (a² - 2ab + b2) + (b² - 2bc + c²) + (c² - 2ac +

a²) = 0

=> (a-b)² + (b-c)² + (c-a)² = 0

=> a - b = 0, b - c = 0, c - a = 0

=> a = b, b = c and c = a => a = b = c

• Therefore, a = b = c