Question

9.
If a² + b2 + c2 - ab – bc - ca = 0, prove that a = b = c.​

Answer 1

Answer:

Step-by-step explanation:

Consider, a  

2

+b  

2

+c  

2

–ab–bc–ca=0

Multiply both sides with 2, we get

2(a  

2

+b  

2

+c  

2

–ab–bc–ca)=0

⇒ 2a  

2

+2b  

2

+2c  

2

–2ab–2bc–2ca=0

⇒ (a  

2

–2ab+b  

2

)+(b  

2

–2bc+c  

2

)+(c  

2

–2ca+a  

2

)=0

⇒ (a–b)  

2

+(b–c)  

2

+(c–a)  

2

=0

Since the sum of square is zero then each term should be zero

⇒ (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

∴ a=b=c.