Question

if a²+b²+c²-ab-bc-ca=0 then ​

Answer 1

Step-by-step explanation:

mere ko bhi nahi ata

Answer 2

Given,

a2+b2+c2−ab−bc−ca=0

Multiply both sides by 2 .

⟹2a2+2b2+2c2−2ab−2bc−2ca=0×2=0

Rearrange as follows,

⟹a2−2ab+b2+b2−2bc+c2+a2−2ca+c2=0

⟹(a2−2ab+b2)+(b2−2bc+c2)+(a2−2ac+c2)=0

⟹(a−b)2+(b−c)2+(a−c)2=0

( Since (A−B)2=A2−2AB+B2)

∵ In the above equations the three quantities namely (a−b)2,(b−c)2 & (a−c)2 are squared terms and are therefore positive. But on the right hand size we have 0 these terms could only be 0 if the individual terms are 0 . i.e.,

a−b=0∣b−c=0∣a−c=0

⟹a=b∣b=c∣a=c

⟹a=b=c

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