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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) = 3 abc`

Text Solution

Verified by Experts

The correct Answer is:
C
(i) Apply the method of cross multiplication and get the desired condition.
(ii) Two equation have more than one solution, it they represent a single line.
(iii) Use, ratio of coefficients of `x `= ratio of coefficients of `y`= ratio of constants and find `a and b`.
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