Mathematics

If (a² + b² + c²) = 89 and (ab - bc - ca) = 16, find the value of (a + b - c).

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Given,

(a² + b² + c²) = 89

(ab - bc - ca) = 16

Using identity,

⇒ (a + b - c)² = (a² + b² + c²) + 2 (ab - bc - ca)

⇒ (a + b - c)² = (89) + 2 (16)

⇒ (a + b - c)² = 89 + 32

⇒ (a + b - c)² = 121

⇒ (a + b - c) = $\sqrt{121}$

⇒ (a + b - c) = $\pm 11$

Hence, (a + b - c) = $\pm 11$ .

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