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705-805 (Hard)|   Algebra|      
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Bunuel
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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 22 Jan 2021, 09:00
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75% (hard)

Question Stats:

52% (02:03) correct 48% (01:57) wrong based on 189 sessions

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If \(abc ≠ 0\) and \(a + b + c = 0\) then what is value of \(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\) ?

A. 0
B. 1
C. 2
D. 3
E. 4
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D
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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 22 Jan 2021, 09:19
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x^3+y^+z^3 - 3xyz = (x+y+z)(x^2+y^2+z^2+xy+yz+xz)
here x+y+z=0
so x^3+y^3+z^3=3xyz

a^2/bc + b^2/ac +c^2/ab = a^3+b^3+c^3 / acb

So from above formula ,
Ans =3
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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 24 Jan 2021, 13:43
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Bunuel
If \(abc ≠ 0\) and \(a + b + c = 0\) then what is value of \(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\) ?

A. 0
B. 1
C. 2
D. 3
E. 4
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Put numbers -1, 2 and 1 for a, b and c and solve it (as long as it satisfies main equation), this is the easiest way i found.
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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 24 Jan 2021, 22:03
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Since its a What is Value question means any value you take and it should satisfy the equation of A + B + C = 0 . All the answers would be same

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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 26 Jan 2021, 05:59
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Bunuel
If \(abc ≠ 0\) and \(a + b + c = 0\) then what is value of \(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\) ?

A. 0
B. 1
C. 2
D. 3
E. 4
Show more
Solution:

We can let a = 1, b = 1 and c = -2. Therefore, the given expression becomes:

1^2/(1 x -2) + 1^2/(-2 x 1) + (-2)^2/(1 x 1)

= -1/2 - 1/2 + 4

= 3

Note that it doesn’t matter what values you choose for a, b, and c; as long as they add to 0, the answer to the addition problem will always be 3.

Answer: D
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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 11 May 2023, 06:00
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Asked: If \(abc ≠ 0\) and \(a + b + c = 0\) then what is value of \(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\) ?

\(\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\frac{a^3}{abc} + \frac{b^3}{abc} + \frac{c^3}{abc} = \frac{a^3 + b^3 + c^3}{abc} = \)

Let us take A=1; B=1; C=-2

\(\frac{a^3 + b^3 + c^3}{abc} = \frac{1+1-8}{-2}) = 3\)

IMO D
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If abc ≠ 0 and a + b + c = 0 then what is value of a^2/bc + b^2/ca + c 29 May 2025, 02:23
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