After comparison of both the equations we conclude both the equation have the same potential solution, but equation A might have the extraneous solution.
What is equation?
" Equation is defined as the algebraic expression which represents the relation between the variables using sign of equality."
According to the question,
Given equations,
Equation A : [tex]\sqrt{x^{2} +3x-6} = \sqrt{x +2}[/tex]
Equation B : [tex]\sqrt[3] {x^{2} +3x-6} = \sqrt[3]{x +2}[/tex]
Solving equation A by finding square root gives two values ± , one of the solution may not be the part of the solution , it is extra .
Therefore , equation with square root might have the extraneous solution.
Else solution is same in both the cases.
Take cube both the side of equation B we get,
[tex]{x^{2} +3x-6} = {x +2}\\\\\implies x^{2} +3x-6 -x-2=0\\\\\implies x^{2} +2x-8=0\\\\\implies x^{2} +4x-2x-8=0\\\\\implies (x+4)(x-2)=0\\\\\implies x= -4 or x=2[/tex]
Hence, after comparison of both the equations we conclude both the equation have the same potential solution, but equation A might have the extraneous solution.
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