Question
Download Solution PDF3x2 – ax + 6 = ax2 + 2x + 2 ന് ഒരേയൊരു (ആവർത്തിച്ചുള്ള) പരിഹാരം മാത്രമേ ഉള്ളൂ എങ്കിൽ, a യുടെ പോസിറ്റീവ് ഇന്റഗ്രൽ സൊല്യൂഷൻ ഇതാണ്:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFനൽകിയിരിക്കുന്നത്:
3x2 – ax + 6 = ax2 + 2x + 2
⇒ 3x2 – ax2 – ax – 2x + 6 – 2 = 0
⇒ (3 – a)x2 – (a + 2)x + 4 = 0
ഉപയോഗിച്ച ആശയം:
ഒരു രണ്ടാംകൃതി സമവാക്യത്തിന് (ax2 + bx + c=0) തുല്യ മൂലങ്ങളുണ്ടെങ്കിൽ, ഡിസ്ക്രിമിനന്റ് പൂജ്യമായിരിക്കണം അതായത്, b2 – 4ac = 0
കണക്കുകൂട്ടൽ:
⇒ D = B2 – 4AC = 0
⇒ (a + 2)2 – 4(3 – a)4 = 0
⇒ a2 + 4a + 4 – 48 + 16a = 0
⇒ a2 + 20a – 44 = 0
⇒ a2 + 22a – 2a – 44 = 0
⇒ a(a + 22) – 2(a + 22) = 0
⇒ a = 2, -22
∴ a യുടെ പോസിറ്റീവ് ഇന്റഗ്രൽ സൊല്യൂഷൻ = 2 ആണ്.Last updated on Jun 11, 2025
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