If a = 0.25, b = -0.05, and c = 0.5, find the value of (a² – b² – c² – 2bc) / (a² – b² – 2ab – c²).
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Correct answer: A
Explanation
a = 0.25 = 1/4
b = −0.05 = −1/20
c = 0.5 = 1/2
(a² − b² − c² − 2bc) / (a² − b² − 2ab − c²)
Numerator -
= (1/4)² − (−1/20)² − (1/2)² − 2(−1/20)(1/2)
= 1/16 − 1/400 − 1/4 + 1/20
= (25 − 1 − 100 + 20)/400
= −56/400
= −14/100
Denominator -
= (1/4)² − (−1/20)² − 2(1/4)(−1/20) − (1/2)²
= 1/16 − 1/400 + 1/40 − 1/4
= (25 − 1 + 10 − 100)/400
= −66/400
(−56/400) ÷ (−66/400)
= 56/66 = 28/33