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Common Difference

137.If ab/ a ...

Question

137.If ab/ a + b = 2, ac/ a + c = 5, bc/ b + c = 9 then find a + b + c

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a + b + c = 9

a b + b c + a c = 26

a^{2} + b^{2} + c^{2}

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ

A = ∣ ∣ ∣ ∣ \begin{matrix} a & c^{2} & c a b & a & b b c & a c & a \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} a & a b & b c b & b c & c c & b & a \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} & c & b b + c^{2} & a + b c & a c + c c & b & a \end{matrix} ∣ ∣ ∣ ∣ ∣,

A

is divisible by

Q. If the vectors

(- b c, b^{2} + b c, c^{2} + b c), (a^{2} + a c, - a c, c^{2} + a c)

(a^{2} + a b, b^{2} + a b, - a b)

are coplanar (where none of a, b or c is zero). Then?

a^{2} + b^{2} + c^{2} - a b - b c - a c = 0

a = 5

b^{2} + c^{2}

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