यदि \(x=\sqrt{3}+\sqrt{2}\), तो \(x^4-10x^2+1\) का मान क्या है?
If \(x=\sqrt{3}+\sqrt{2}\), what is the value of \(x^4-10x^2+1\)?
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Correct Answer
A. (0)
Concept
\(x^2=5+2\sqrt{6}\).
Why this answer is correct
Using the identity \(x^2+\frac{1}{x^2}=10\), we get \(x^4-10x^2+1=0\).
Exam Tip
In such questions, recognize the relation between (x) and its conjugate reciprocal. चरण 1: \(x^2=5+2\sqrt{6}\) है। चरण 2: \(x^2+\frac{1}{x^2}=10\) की पहचान से \(x^4-10x^2+1=0\) मिलता है। चरण 3: ऐसे प्रश्नों में (x) और उसके संयुग्मी व्युत्क्रम का संबंध पहचानें।
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