Conversion ${\left( {x - a} \right)^4} + {\left( {x - b} \right)^4} = A$ into polynomial of degree 2

Asked Aug 05 '20 at 06:24

Active Aug 05 '20 at 06:24

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Convert the following polynomial of degree 4 ${\left( {x - a} \right)^4} + {\left( {x - b} \right)^4} = A$ into polynomial of degree 2

My approach is as follow

$y = \frac{{{{\left( {x - a} \right)}^2} + {{\left( {x - b} \right)}^2}}}{2}$

$4{y^2} = {\left( {x - a} \right)^4} + {\left( {x - b} \right)^4} + 2{\left( {x - a} \right)^2}{\left( {x - b} \right)^2}$

$\Rightarrow 4{y^2} = A + 2{\left( {x - a} \right)^2}{\left( {x - b} \right)^2}$

After this step I am not able to proceed

asked Aug 05 '20 at 06:24

Samar Imam Zaidi

2

Set $y=\left(x-\frac{a+b}{2}\right)^2$. – Omran Kouba Aug 05 '20 at 06:28
As asked, the question does not make much sense, you can't change the degree of a polynomial. And you don't turn an equation into a polynomial. – Aug 05 '20 at 06:41
I want to convert in into two degree equation – Samar Imam Zaidi Aug 05 '20 at 06:43
Erase $4$ and write $2$. – cgiovanardi Aug 06 '20 at 00:03

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