Question
Download Solution PDFयदि x2 - 1, 2x और x2 + 1 एक समकोण त्रिभुज की तीन भुजाएँ हैं, तो निम्नलिखित में से कौन इसका कर्ण हो सकता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
समकोण त्रिभुज की तीन भुजाएँ: x2 - 1, 2x, x2 + 1
प्रयुक्त सूत्र:
समकोण त्रिभुज में, कर्ण का वर्ग, अन्य दो भुजाओं के वर्गों के योग के बराबर होता है।
गणना:
कर्ण2 = भुजा 12 + भुजा 22
मान लीजिए x2 + 1 कर्ण है।
⇒ (x2 + 1)2 = (x2 - 1)2 + (2x)2
⇒ (x2 + 1)2 = x4 - 2x2 + 1 + 4x2
⇒ x4 + 2x2 + 1 = x4 + 2x2 + 1
⇒ चूँकि, बायाँ पक्ष = दायाँ पक्ष
⇒ इसलिए, कर्ण2 = भुजा 12 + भुजा 22
⇒ अतः, (x2 + 1) दिए गए त्रिभुज का कर्ण है।
∴ सही उत्तर x2 + 1 है।
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