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At which values of \(x\) do the graph of \(y=|x-2|\) and the line \(y=4\) intersect?ग्राफ़ \(y=|x-2|\) और रेखा \(y=4\) किन \(x\) मानों पर प्रतिच्छेद करते हैं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x=-2,6\)\(x=-2,6\)
At an intersection, the two graphs have the same \(y\)-value, so \(|x-2|=4\). Thus \(x-2=4\) or \(x-2=-4\), giving \(x=6\) or \(x=-2\). Therefore, option A is correct. Option B does not satisfy \(|x-2|=4\). Exam tip: when \(|u|=a\) with \(a>0\), solve both cases \(u=a\) and \(u=-a\).प्रतिच्छेद बिंदुओं पर दोनों समीकरणों के \(y\) मान समान होंगे, इसलिए \(|x-2|=4\)। इससे \(x-2=4\) या \(x-2=-4\), अतः \(x=6\) या \(x=-2\)। इसलिए सही विकल्प A है। विकल्प B में \(|x-2|=4\) का सही हल नहीं मिलता। परीक्षा-युक्ति: \(|u|=a\), जहाँ \(a>0\), हो तो हमेशा \(u=\pm a\) के दोनों मामले जाँचें।
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