Bihar Police Constable practice question
Given a = 4 + √15, determine the value of a³ + 1/a³.
From a Bihar Police Constable Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (B) 488
Given a = 4 + √15. Since (4 + √15)×(4 − √15) = 4² − 15 = 1, we get 1/a = 4 − √15.
So a + 1/a = 8.
Using a³ + 1/a³ = (a + 1/a)³ − 3(a + 1/a):
a³ + 1/a³ = (8)³ − 3×(8) = 488.
हिंदी में प्रश्न
दिया गया है कि a = 4 + √15। a³ + 1/a³ का मान निर्धारित कीजिए।
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सही उत्तर: (B) 488
दिया है a = 4 + √15। चूँकि (4 + √15)×(4 − √15) = 4² − 15 = 1, इसलिए 1/a = 4 − √15।
अतः a + 1/a = 8।
सर्वसमिका a³ + 1/a³ = (a + 1/a)³ − 3(a + 1/a) का प्रयोग करने पर:
a³ + 1/a³ = (8)³ − 3×(8) = 488।
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