Question
Download Solution PDFयदि ax2 + bx + c = 0 और bx2 + cx + a = 0 का एक उभयनिष्ठ मूल a ≠ 0 है तो
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
1. एक और दो सामान्य जड़ों के लिए शर्त:
यदि दोनों मूल उभयनिष्ठ हैं, तो स्थिति निम्न है
2. a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
अगर a = b = c, तो
a3 + b3 + c3 = 3abc
गणना:
मान लें कि,
ax2 + bx + c = 0 ----(1)
bx2 + cx + a = 0 ----(2)
प्रश्न के अनुसार, समीकरण (1) और (2) के दोनों मूल उभयनिष्ठ हैं। इसलिए, ऊपर चर्चा की गई अवधारणा का उपयोग करते हुए
यह तभी संभव होगा जब
⇒ a = b, b = c, c = a
⇒ a3 + b3 + c3 = 3abc
⇒
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