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यदि समीकरण (a + b)x2 – 2(ac + bd) x + (c2 + d2) = 0 के मूल बराबर हैं, तो सिद् कीजिए कि a/b = c/d |
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Answer» समीकरण (a2 + b2)x2 – 2(ac + bd)x + (c2 + d2) = 0 A = a2 + b2, B = – 2(ac + bd), C = (c2 + d2) ∵ समीकरण के मूल बराबर हैं। ∴ B2 – 4AC = 0 [- 2 (ac + bd)]2 – 4(a2 + b2)(c2 + d2) = 0 4(ac + bd)2 – 4(a2c2 + a2d2 + b2c2 + b2d2)= 0 4[a2c2 + b2d2 + 2acbd – a2c2 – a2d2 – b2c2 – b2d2] = 0 -a2d2 – b2c2 + 2acbd = 0 – [(ad)2 + (bc)2 – 2acbd] = 0 (ad – bc)2 = 0 ad – bc = 0 ad = bc a/b = c/d इति सिद्धम्। |
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