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If bc + ca + ab = 0, find the value of bc/a^2 + ca/b^2 + ab/c^2 a. -2 b. 2 c. 3 d. -3

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nasirjam | Student, Grade 9

Posted April 9, 2013 at 11:52 AM via web

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

a. -2

b. 2

c. 3

d. -3

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pramodpandey | College Teacher

Posted April 9, 2013 at 1:05 PM (Answer #1)

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`ab+bc+ca=0`

`ab+bc=-ca`

`(ab+bc)^3=(-ca)^3`

`(ab)^3+(bc)^3+3abxxbc(ab+bc)=-(ca)^3`

`(ab)^3+(bc)^3+3acb^2(-ca)+(ca)^3=0`

`(ab)^3+(bc)^3+(ca)^3=3a^2b^2c^2`

Divide both side by `a^2b^2c^2`

`(ab)^3/(a^2b^2c^2)+(bc)^3/(a^2b^2c^2)+(ca)^3/(a^2b^2c^2)=3`

`(ab)/c^2+(bc)/a^2+(ca)/b^2=3`

`(bc)/a^2+(ca)/b^2+(ab)/c^2=3`

Ans. C

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