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If the ordered pair (p, q) satisfies the...

If the ordered pair (p, q) satisfies the simultaneous equations `(a + b)x + (b + c)y + (c + a) = 0` and `(b + c)x + (c +a)y + (a + b) = 0` such that p and q are in the ratio 1:2, then which of the following is correct?

A

`a^2 + 2ac + 3c^2 = 2b^2 + 3ab + bc`

B

`a^2 + b^2 + c^2 = ab + bc + ca`

C

`a^2 + 3ac + 3c^2 = 3b^2 + 3ab + bc `

D

`a^3+b^3+c^3=3abc`

Text Solution

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The correct Answer is:
c
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If the ordered pair (p,q) satisfies the simultaneous equations (a+b)x+(b+c)y+(c+a)=0 and (b+c)x+(c+a)y+(a+b)=0 such that p and q are in the ratio1:2,then which of the following is correct?

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Knowledge Check

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    B
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    C
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    A
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    C
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  • If a+b+c=0, a,b,c in Q then roots of the equation (b+c-a) x ^(2) + (c+a-c) =0 are:

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    B
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