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If a + B + C = 0 and A2 + B2 + C2 = 16, Find the Value of Ab + Bc + Ca.

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Question

If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.

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Solution

We know that,

`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`

`=> (0)^2 = 16 + 2(ab + bc + ca)`    `[∵ a + b + c = and a^2 + b^2 + c^2 = 16] `

=> 2(ab + bc + ca) = -16

=> ab + bc + ca = -8

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Chapter 4: Algebraic Identities - Exercise 4.2 [Page 12]

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R.D. Sharma Mathematics [English] Class 9
Chapter 4 Algebraic Identities
Exercise 4.2 | Q 2 | Page 12

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