Is there any difference b/w an equation and an identity? Thanks,

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neela | High School Teacher | (Level 3) Valedictorian

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There is difference between an equation and an identity.

The equation is true conditionally. Whereas the identity is true always.

The equation is true for  particular values of the variable(or variables). But an identity is true for all values.

An identity is an equation , in which the right side is derivable from left, and the left side is derivable from the right. Not so in case of an equation.

Examples: 3x+6=9 is an equation. It is condtionally true for x=1. It is not true for 2 or 3 or for any x other than 1.

(x+1)^2 = x^2+2x+1 is an identity and true for all values of x.

3x+y = 4 is an equation straight line representing a straight line is conditionally true for all the points on that graph. But go out of the graph and chose x=10 y= 10, the equation is not true.

x^3+8y^3 = (x^2-2xy+4x^2)(x+2y)  is an identity and therefore true for all values of x and y.Proof: (a^+b^3 )/(a+b) = a^2-ab+b^2. Put a=x and b=2y, Then {(x^3+(2y)^3]/(x+2y) = x^2-x(2y)+(4y)^2. Therefore,

x^3+8y^3 = (x^2-2xy+4x^2)(x+2y).