Question
Download Solution PDFयदि (x - 1)2 + (y - 2)2 = (x – 1) (y - 2), जहाँ x और y पूर्णांक हैं, तो 2x + 3y का मान है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है,
(x - 1)2 + (y - 2)2 = (x – 1) (y - 2)
गणना:
(x - 1)2 + (y - 2)2 = (x – 1) (y - 2)
यह x और y के सभी वास्तविक मानों के लिए हमेशा सत्य होगा।
तो, यदि x = 1
⇒ (1 - 1)2 + (y - 2)2 = (1 – 1) (y - 2)
⇒ (y - 2)2 = 0
⇒ y = 2
⇒ 2x + 3y = 2 × 1 + 3 × 2
⇒ 2x + 3y = 8
Alternate Method
दिया गया है,
(x - 1)2 + (y - 2)2 = (x – 1) (y - 2)
अवधारणा:/सूत्र:
(x – y)2 = k2
(x – y) = k या (–k)
x = (k + y) या (y – k)
गणना:
(x -1)2 + (y - 2)2 = (x – 1) (y - 2)
लेते हैं,
⇒ (x – 1)2 = (x – 1) (y – 2)
⇒ (x – 1) = (y – 2)
⇒ x – y = -2 + 1
⇒ x – y = (-1) ----(1)
लेते हैं,
⇒ (y – 2)2 = (x – 1) (y – 2)
⇒ (y – 2) = (x – 1)
⇒ x – y = -2 + 1
⇒ x – y = (-1) ----(2)
मान लीजिये y = 2 और x = 1, तो
⇒ 1 – 2 = (-1)
(-1) = (-1) (संतुष्ट)
अब,
2x + 3y
⇒ 2 × 1 + 3 × 2
⇒ 2 + 6
⇒ 8
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