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Mathematics

If a − b + c = 6 and a2 + b2 + c2 = 38, then ab + bc − ca is :

  1. 0

  2. 1

  3. -1

  4. not possible

Expansions

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Answer

Given,

a - b + c = 6

a2 + b2 + c2 = 38

We know that,

⇒ [(a - b) + (c)]2 = (a - b)2 + c2 + 2 × (a - b) × c

⇒ [(a - b) + (c)]2 = a2 + b2 - 2 × a × b + c2 + 2ac - 2bc

⇒ (6)2 = a2 + b2 + c2 - 2(ab - ac + bc)

⇒ 36 = 38 - 2(ab - ac + bc)

⇒ 2(ab + bc − ca) = 38 - 36

⇒ 2(ab + bc − ca) = 2

⇒ (ab + bc − ca) = 22\dfrac{2}{2}

⇒ (ab + bc − ca) = 1.

Hence, Option 2 is the correct option.

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