IB ACIO Grade II previous year question
What is the cube root of (5√5 × 11√11) − (17√17) − (3√5 × √11 × √17)[√5 × √11 − √17]?
Asked in IB ACIO Grade II (16 Sep 2025 Shift 2) · Quantitative Aptitude
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Correct answer: (D) √55 − √17
Let a=√5, b=√11, c=√17. Expression = a³b³ − c³ − 3ab·c(ab−c) = (ab)³ − c³ − 3(ab)²c + 3ab·c² = (ab − c)³ (using the identity x³−y³−3xy(x−y) = (x−y)³ with x=ab, y=c). So the expression = (ab−c)³ = (√55 − √17)³. Cube root = √55 − √17.
हिंदी में प्रश्न
(5√5 × 11√11) − (17√17) − (3√5 × √11 × √17)[√5 × √11 − √17] का घनमूल ज्ञात कीजिए।
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सही उत्तर: (D) √55 − √17
मान लें a=√5, b=√11, c=√17। व्यंजक = a³b³ − c³ − 3ab·c(ab−c) = (ab)³ − c³ − 3(ab)²c + 3ab·c² = (ab−c)³ (सर्वसमिका x³−y³−3xy(x−y)=(x−y)³ का प्रयोग करते हुए, जहाँ x=ab, y=c)। अतः व्यंजक = (ab−c)³ = (√55−√17)³। घनमूल = √55 − √17।
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