AP Police SI previous year question
If a + b = 1 and a² + b² = 2, then a⁵ + b⁵ =
Asked in AP Police SI Prelims: 2023 (Paper I & II) · Quantitative Aptitude
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Correct answer: (B) 19/4
ab = [(a+b)² − (a²+b²)]/2 = (1−2)/2 = −1/2. Using Newton's identities: s₃ = s₁s₂ − p·s₁ = 2 − (−1/2)(1) = 2.5; s₄ = s₁s₃ − p·s₂ = 2.5 + 1 = 3.5; s₅ = s₁s₄ − p·s₃ = 3.5 + 1.25 = 4.75 = 19/4.
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हिंदी में प्रश्न
यदि a + b = 1 और a² + b² = 2 है, तो a⁵ + b⁵ =
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (B) 19/4
ab = [(a+b)² − (a²+b²)]/2 = (1−2)/2 = −1/2। न्यूटन के सर्वसमिकाओं का उपयोग करते हुए: s₃ = s₁s₂ − p·s₁ = 2 − (−1/2)(1) = 2.5; s₄ = s₁s₃ − p·s₂ = 2.5 + 1 = 3.5; s₅ = s₁s₄ − p·s₃ = 3.5 + 1.25 = 4.75 = 19/4।
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