Question
Download Solution PDFयदि x + y = 36 है, तो ((x - 27)3 + (y - 9)3 ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
x + y = 36
प्रयुक्त सूत्र:
a3 + b3 = (a + b)(a2 - ab + b2)
गणना:
⇒ x + y = 36
⇒ x + y - 36 = 0 ................(1)
⇒ (x - 27) + (y - 9) = 0
माना (x - 27) = a और y - 9 = b
a3 + b3 = (a + b)(a2 + b2 - ab) सूत्र का उपयोग करके, a और b का मान समीकरण में प्रतिस्थापित करें
⇒ (x - 27)3 + (y - 9)3 = ( x - 27 + y - 9)((x - 27)2 - (x - 27)(y - 9) + (y - 9)2)
⇒ (x - 27)3 + (y - 9)3 = ( x + y - 36)((x - 27)2 - (x - 27)(y - 9) + (y - 9)2)
समीकरण (1) से x + y - 36 = 0 का मान
⇒ (x - 27)3 + (y - 9)3 = (0)((x - 27)2 - (x - 27)(y - 9) + (y - 9)2)
⇒ (x - 27)3 + (y - 9)3 = 0
∴ अभीष्ट मान 0 है।
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