Question

(b) If the same pair of values of x, y satisfy the three equations
ax + by + C = 0
bx + cy+ a = 0
cx + ay+b=0
then find the relation between a, b, c,​

Answer 1

answer

ax + by + c = 0

step by step explanation

bx + cy + a = 0

cx + ay + b = 0

Adding all the above equations, we get,

ax + by + c + bx + cy + a + cx + ay + b = 0

ax + ay + a + bx + by + b + cx + cy + c = 0

a(x + y + 1) + b(x + y + 1) + c(x + y + 1) = 0

(x + y + 1)(a + b + c) = 0

Assuming, (a + b + c) = 0, we get,

a + b = -c ... (1)

Cubing both sides,

a^3 + b^3 + 3ab(a + b) = -c^3

a^3 + b^3 + 3ab(-c) = -c^3 ... from eq. (1)

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

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

If, (x + y + 1), then a, b and c doesn't satisfy the given equation.

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