Find the value of ab – bc – ca.

If a + b – c = 5 and a² + b² + c² = 29, find the value of ab – bc – ca.

Answer :

It is given that

a + b – c = 5

By squaring on both sides

(a + b – c)² = 5²

Expanding using formula

a² + b² + c² + 2ab – 2bc – 2ca = 25

Substituting the values and taking 2 as common

29 + 2 (ab – bc – ca) = 25

By further calculation

2 (ab – bc – ca) = 25 – 29 = – 4

So we get

ab – bc – ca = – 4/2 = – 2

Therefore, ab – bc – ca = – 2.

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