If (a − b −c)² = 49 and bc −ac − ab = 12, then what is the value of the expression a² + b² + c²?

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Solution

The correct option is B
25

It is known that: (a − b − c)² = a² + b² + c² − 2ab + 2bc − 2ac

∴(a − b − c)² = a² + b² + c² + 2 (bc − ac − ab)

⇒ a² + b² + c² = (a − b − c)² − 2 (bc − ac − ab)

= 49 − 2(12) [(a − b −c)² = 49, bc −ac − ab = 12]

= 25

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