If 24√3x3+5√5y3 = (2√3x+√5y) x (Ax²-Bxy+Cx²), then what is the value of (A2-B2+C2)?
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Correct answer: C
Explanation
The correct answer is Option 3 i.e. 109.
24√3x³ + 5√5y³ = (2√3x + √5y)(Ax² − Bxy + Cy²)
= 2A√3x³ − 2B√3x²y + 2C√3xy² + A√5x²y − B√5xy² + C√5y³
x³: 2A√3 = 24√3 → A = 12
y³: C√5 = 5√5 → C = 5
x²y: −2B√3 + 12√5 = 0
⇒ −2B√3 = −12√5 → B = 6√(5/3)
A² − B² + C² = 144 − (6√(5/3))² + 25
= 144 − 36×5/3 + 25 = 144 − 60 + 25 = 109