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

By K Balaji|Updated : November 12th, 2022

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

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.

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