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If a+b+c=0, then find the value of a^2+b^2+c^2/a^2-bc

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madmoni06 | Student | Honors

Posted April 1, 2013 at 6:19 PM via web

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If a+b+c=0, then find the value of a^2+b^2+c^2/a^2-bc

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pramodpandey | College Teacher | Valedictorian

Posted April 2, 2013 at 10:50 AM (Answer #1)

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a+b+c=0

`(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc`

`a^2+b^2+c^2+2ab+2ac+2bc=0`

`a^2+b^2+c^2=-(2ab+2ac+2bc)`

`a^2+b^2+c^2=-2(ab+ac+bc)`      (i)

also

`a=-b-c`

`a^2=-ab-ac`                                  (ii)

`-c=a+b`

`-bc=ab+b^2`                                 (iii)

adding  (ii) and (iii) ,we have

`a^2-bc=b^2-ac`                            (iv)

devide (i) by (iv)

`(a^2+b^2+c^2)/(a^2-bc)=(-2(ab+bc+ca))/(b^2-ac)`

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