यदि `a^(2)+b^(2)+c^(2)-ab-bc-ca=0` तो `a:b:c` क्या होगा?

Options

A. `1:2:1`
B. `2:1:1`
C. `1:1:2`
D. `1:1:1`

Answer

D

Explanation

Given
`a^(2)+b^(2)+c^(2)-ab-bc-ca=0`
to find `a:b:c=?`
`implies` According to the question
`a^(2)+b^(2)+c^(2)-ab-bc=ca=0`
`implies a^(2)+b^(2)+c^(2)=ab+bc+ca`
`implies` Let `a=b=c=1`
`implies 1^(2)+1^(2)+1^(2)=1xx+(1xx1)+(1xx1)`
`implies 3=3`
`implies` So ratio of `a:b:c=1:1:1`