Question

if a^2+b^2+c^2-ab-bc-ca=0, then






plz do help me ​

Answer 1

CORRECT QUESTION:

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

TO PROVE:  

a=b=c

GIVEN:

a²+b²+c²-ab-bc-ca=0

FORMULA

(x-y)²=x²+y²-2xy

Explanation:

Multiply by 2 on both sides in the given equation.  

2a²+2b²+2c²-2ab-2bc-2ca =0

ARRANGE IN ORDER

a²+b²+-2ab+b²+c²-2bc+a²+c²-2ca =0

(a-b)²+(b-c)²+(c-a)²=0.

THE SUM OF THE SQAURES CAN BE ZERO ONLY WHEN THE SQAURE IS EQUAL TO ZERO.HENCE

(a-b)² =0.          (b-c)²=0.            (c-a)²=0.

a-b =  0.         b-c=0.             c-a=0  

a = b             b = c               c = a

 FROM ABOVE WE CAN CONCLUDE THAT  a = b = c  

HENCE VERIFIED