Question

If a,b,c are real numbers and a^2+b^2+c^2-ab-bc-ca=0,then show that a=b=c

Answer 1

Answer:

Step-by-step explanation:

Proof by reverse assumption method

let us assume that a = b = c,

that is a = b

           a = c

so when we take the expression a²+b²+c²-ab-bc-ac,

the same will be written as,

a² + a² + a² - a*a - a*a - a*a

=> 3a² - a² - a² -a²

=> 3a² - 3a²

= 0

so, a²+b²+c²-ab-bc-ac = 0 if a = b = c

and therefore

if a²+b²+c²-ab-bc-ac=0 then a = b = c