Equations Which Can Be Reduced to Linear, Quadratic and Biquadratic Equations
Category : JEE Main & Advanced
Type I : An equation of the form
\[(x-a)\,(x-b)\,(x-c)\,(x-d)=A\],
where \[a<b<c<d\], \[b-a=d-c\], can be solved by a change of variable.
i.e.,\[y=\frac{(x-a)+(x-b)+(x-c)+(x-d)}{4}\]
\[y=x-\frac{(a+b+c+d)}{4}\].
Type II : An equation of the form
\[(x-a)\,(x-b)(x-c)(x-d)=A{{x}^{2}}\]
where \[ab=cd\], can be reduced to a collection of two quadratic equations by a change of variable \[y=x+\frac{ab}{x}\].
Type III : An equation of the form \[{{(x-a)}^{4}}+{{(x-b)}^{4}}=A\] can also be solved by a change of variable, i.e., making a substitution \[y=\frac{(x-a)+(x-b)}{2}\].
You need to login to perform this action.
You will be redirected in
3 sec
