Theorem 1 If

MATHEMATICS · Subjective · CBSE · Mathematics · We Distribute, Yet Things Multiply · We Distribute, Yet Things Multiply

Problem

Theorem 1 If

(\sqrt{P} + Q)^n = I + f

, where

I

and

n

are positive integers,

n

being odd and

0 \le f < 1

, then show that

(I + f)f = k^n

, where

P - Q^2 = k > 0

and

\sqrt{P} - Q < 1

.

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