यदि \(a+b\sqrt{2}=0\) है जहां (a) और (b) परिमेय हैं तथा \(b\neq 0\) है तो क्या निष्कर्ष निकलेगा?
If \(a+b\sqrt{2}=0\) where (a) and (b) are rational and \(b\neq 0\) then what conclusion follows?
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}=-\frac{a}{b}\) परिमेय होगा जो असंभव है\(\sqrt{2}=-\frac{a}{b}\) would be rational which is impossible
Concept
The equation gives \(\sqrt{2}=-\frac{a}{b}\).
Why this answer is correct
\(-\frac{a}{b}\) is rational but \(\sqrt{2}\) is irrational.
Exam Tip
Such questions use irrationality to create a contradiction. चरण 1: समीकरण से \(\sqrt{2}=-\frac{a}{b}\) मिलेगा। चरण 2: \(-\frac{a}{b}\) परिमेय है लेकिन \(\sqrt{2}\) अपरिमेय है। चरण 3: ऐसे प्रश्नों में अपरिमेयता से विरोधाभास बनता है।
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