If a² + b² + c² = 240 and ab - bc - ca = 64, then find the value of (a + b - c)².
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Correct answer: A
Explanation
Given:
a² + b² + c² = 240
ab − bc − ca = 64
By the formula:
(a + b − c)² = a² + b² + c² + 2ab − 2ac − 2bc
(a + b − c)² = a² + b² + c² + 2ab − 2ac − 2bc
= 240 + 2(ab − ac − bc)
= 240 + 2(64)
= 240 + 128
= 368