(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,
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Answer:
ax + by + c = 0
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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Answer:DOESNT SATISIFY
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