Question

If a + b + c = 9 and AB + BC + CA = 40 then the value of a square + b square + c square

Answer 1

a + b + c = 9

ab + bc + ca = 40

To find : a² + b² + c²

The following expression matches to the algebraic identity

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

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

Thus,

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

substituting the values,

we have,

9² = a² + b² + c² + 2( 40)

81 = a² + b² + c² + 80

Transposing 80 to LHS,

we have,

81 - 80 = a² + b² + c²

Thus,

a² + b² + c² = 1

Answer 2

Step-by-step explanation:

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