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If \(x=\sqrt{7}-\sqrt{3}\), what is the value of \(x^{2}+2\sqrt{21}\)?यदि \(x=\sqrt{7}-\sqrt{3}\) है, तो \(x^{2}+2\sqrt{21}\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1010
Squaring the given expression, \(x^{2}=(\sqrt{7}-\sqrt{3})^{2}=7+3-2\sqrt{21}=10-2\sqrt{21}\). Therefore, \(x^{2}+2\sqrt{21}=10\), so option C is correct. Exam tip: While using \((a-b)^2=a^2+b^2-2ab\), take care to retain the negative sign in the middle term.दिए गए मान का वर्ग करने पर \(x^{2}=(\sqrt{7}-\sqrt{3})^{2}=7+3-2\sqrt{21}=10-2\sqrt{21}\)। अतः \(x^{2}+2\sqrt{21}=10\)। इसलिए सही विकल्प C है। परीक्षा-युक्ति: \((a-b)^2=a^2+b^2-2ab\) का प्रयोग करते समय मध्य पद का चिह्न न भूलें।
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