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Cramer's Rule

If p^a = q^b ...

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If p^a = q^b = r^c and pqr= 1 prove that 1/a +1/b+1/c = 0.

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Q. In the Figure, PA, QB and RC are perpendicular to AC. Prove that

\frac{1}{x} + \frac{1}{z} = \frac{1}{y}

.

In Fig. 7.145, PA, QB and RC are each perpendicular to AC. Prove that $\frac{1}{x} + \frac{1}{z} = \frac{1}{y}$

Q. In the given figure, PA, QB and RC are each perpendicular to AC. Prove that

\frac{1}{x} + \frac{1}{z} = \frac{1}{y}

p + q + r = 0

, then prove that

∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣ = p q r ∣ ∣ ∣ ∣ \begin{matrix} a & b & c c & a & b b & c & a \end{matrix} ∣ ∣ ∣ ∣

p + q + r = 0,

∣ ∣ ∣ ∣ \begin{matrix} p a & q b & r c q c & r a & p b r b & p c & q a \end{matrix} ∣ ∣ ∣ ∣ = p q r ∣ ∣ ∣ ∣ \begin{matrix} a & b & c c & a & b b & c & a \end{matrix} ∣ ∣ ∣ ∣

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