If a + b + c = 0 then find a^2/bc + b^2/ac + c^2/ab

By BYJU'S Exam Prep

Updated on: September 25th, 2023

We know that

(a³ + b³ + c³ – 3abc) = (a + b + c) (a² + b² + c² – ab – bc – ac)

Given that a + b + c = 0

Then, a³ + b³ + c³ = 3abc

Now by dividing both sides by abc, we get

a³/3abc + b³/3abc + c³/3abc = 3

On simplifying we get

a²/bc + b²/ac + c²/ab = 3

Table of content

1. If a + b + c = 0 then find a2/bc + b2/ac + c2/ab

Algebraic Identities

Algebraic identities are equations in algebra that are true regardless of the value of each of their variables. Mathematical equations with numbers, variables (unknown values), and mathematical operators are known as algebraic identities and expressions (addition, subtraction, multiplication, division, etc.)

Numerous areas of mathematics, including algebra, geometry, trigonometry, etc., use algebraic identities. These are mostly employed to identify the polynomials’ factors. A deeper comprehension of algebraic identities helps to improve one’s ability to answer sum problems quickly. The factorization of polynomials is one of the most significant uses for algebraic identities.

Two variable identities

The identities in algebra with two variables are as follows. By multiplying polynomials and extending the square or cube, these identities can be easily confirmed.

Three variable identities

Just as the identities for the two variables, the identities for three variables in algebra have also been derived.

Summary:-

If a + b + c = 0 then find a²/bc + b²/ac + c²/ab

If a + b + c = 0 then a²/bc + b²/ac + c²/ab is 3. Equations in algebra that are regardless of the value of each variables is called as algebraic identities.

Related Questions:-

If a + b + c = 0 then find a^2/bc + b^2/ac + c^2/ab

Algebraic Identities

If a + b + c = 0 then find a2/bc + b2/ac + c2/ab

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If a + b + c = 0 then find a²/bc + b²/ac + c²/ab