Question
Download Solution PDFयदि x2 + y2 + z2 = xy + yz + zx और x = 1 है, तो \(\rm \frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}\) का मान ज्ञात कीजिए?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
x = 1
x2 + y2 + z2 = xy + yz + zx
गणना:
x2 + y2 + z2 - xy - yz - zx = 0
⇒(1/2)[(x - y)2 + (y - z)2 + (z - x)2] = 0
⇒x = y , y = z और z = x
लेकिन x = y = z = 1
इसलिए, \(\rm \frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}\)
= {10(1)4 + 5(1)4 + 7(1)4}/{13(1)2(1)2+ 6(1)2(1)2 + 3(1)2(1)2}
= 22/22
= 1
इसलिए, अभीष्ट मान 1 है।
Last updated on Jul 15, 2025
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