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If (a+b\sqrt{2}=0) where (a) and (b) are rational and (b\neq 0) then what conclusion follows?यदि (a+b\sqrt{2}=0) है जहां (a) और (b) परिमेय हैं तथा (b\neq 0) है तो क्या निष्कर्ष निकलेगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\sqrt{2}=-\frac{a}{b}) would be rational which is impossible(\sqrt{2}=-\frac{a}{b}) परिमेय होगा जो असंभव है
Step 1: The equation gives (\sqrt{2}=-\frac{a}{b}). Step 2: (-\frac{a}{b}) is rational but (\sqrt{2}) is irrational. Step 3: 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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