If \(x=-7\), what is the value of \(\sqrt{x^2}-2x\)?यदि \(x=-7\) है, तो \(\sqrt{x^2}-2x\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 2121
Substituting \(x=-7\), we get \(x^2=(-7)^2=49\). Hence, \(\sqrt{x^2}=\sqrt{49}=7\), since the principal square root is non-negative. Also, \(-2x=-2(-7)=14\). Therefore, \(\sqrt{x^2}-2x=7+14=21\). Taking \(-7\) for the square root would be incorrect because \(\sqrt{x^2}=|x|\), not always \(x\). Exam tip: Rewrite \(\sqrt{x^2}\) as \(|x|\) to avoid sign errors.\(x=-7\) रखने पर \(x^2=(-7)^2=49\) होता है। अतः \(\sqrt{x^2}=\sqrt{49}=7\), क्योंकि वर्गमूल का मुख्य मान धनात्मक होता है। साथ ही, \(-2x=-2(-7)=14\)। इसलिए \(\sqrt{x^2}-2x=7+14=21\)। \(-7\) लेना गलत होगा, क्योंकि \(\sqrt{x^2}=|x|\) होता है, न कि हमेशा \(x\)। परीक्षा टिप: \(\sqrt{x^2}\) को \(|x|\) लिखकर चिन्ह की गलती से बचें।
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