  # If a2 + b2 + c2 + 84 = 4 (a – 2b + 4c), then √ab – bc + ca is Equal to

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Updated on: September 25th, 2023 1. 4√10
2. 5√10
3. 2 √10
4. √10

If a2 + b2 + c2 + 84 = 4 (a – 2b + 4c), then √ab – bc + ca is equal to 2 √10

Algebraic identities are algebraic equations that are true regardless of the value of each variable. They are used in the polynomials factorization. Algebraic identities are used in this manner for the computation of numerous algebraic expressions and the solution of various polynomials.

The three mathematical algebraic identities are:

Identity 1: (a+b)2 = a2 + b2 + 2ab

Identity 2: (a-b)2 = a2 + b2 – 2ab

Identity 3: a2 – b2 = (a+b) (a-b)

It is given that

a2 + b2 + c2 + 84 = 4(a – 2b + 4c)

Calculation :

By rearranging

a2 + b2 + c2 + 84 – 4a + 8b -16c = 0

a2 – 4a + 4 +b2 + 8b + 16+ c2 – 16c + 64 = 0

So we get

(a – 2)2 + (b + 4)2 + (c-8)2 = 0

As (a – b)2 + (b – c)2 + (c – a)2 = 0

We get a – b = 0

a = b

b = c

c = a

a = 2, b= -4 and c = 8

√ab – bc + ca = √[(2 x -4) – (8 x -4) + (8 x 2)]

√(-8) – (-32) + 16 = √40

√40 = 2√10

Summary:-

## If a2 + b2 + c2 + 84 = 4 (a – 2b + 4c), then √ab – bc + ca is equal to-1. 4√10 2. 5√10 3. 2 √10 4. √10

√ab – bc + ca is equal to 2√10 if a2 + b2 + c2 + 84 = 4 (a – 2b + 4c)

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