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Numbers in General Form

If a^1/p=b^1/...

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If a^{1/p}=b^{1/q}=c^{1/r} and abc = 1, where a, b & c are distinct positive numbers, then value of (p + q + r) is

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Q. If a, b, c are the sides of a triangle ABC, then

a^{\frac{1}{p}} + b^{\frac{1}{p}} - c^{\frac{1}{p}}

p > 1

Q. If 0. ABC ABC ABC ……..

= \frac{P}{Q},

where A, B and C are distinct positive real numbers and P, Q are prime numbers, then sum of all possible values of P is

यदि 0. ABC ABC ABC ……..

= \frac{P}{Q},

जहाँ A, B व C भिन्न धनात्मक वास्तविक संख्याएँ हैं तथा P, Q अभाज्य संख्याएँ हैं, तब P के सभी संभावित मानों का योगफल है

p, q, r

be three distinct real numbers , then the value of

(p + q) (q + r) (r + p)

\to a, \to b, \to c

are three non-coplanar vectors,

\to p, \to q, \to r

are non-zero vectors such that

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]},

then the value of the expression

(\to a + \to b + \to c), (\to p + \to q + \to r)

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

\to a, \to b

\to c

are three non-coplanar vectors, then the value of the expression

(\to a + \to b + \to c) \cdot (\to p + \to q + \to r)

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