Question
Check whether the given equation is quadratic equation or not: $x^3-4 x^2-x+1=(x-2)^3$
✓
Answer
We have given that, $x^3-4 x^2-x+1=(x-2)^3$
Applying identity on $R.H.S.$ we get,
$(a-b)^{3}=a^{3}-b^{3}-3 a^{2} b+3 a b^{2}$
$\Rightarrow x^{3}-4 x^{2}-x+1=x^{3}-8-6 x^{2}+12 x$
$\Rightarrow x^{3}-4 x^{2}-x+1-x^{3}+8+6 x^{2}-12 x=0$
$\Rightarrow 2 x^{2}-13 x+9=0$
Degree of the equation is $2$ and
It is of the form $a x^{2}+b x+c=0,$ with $a \neq 0$ , therefore, the given equation is quadratic.
Applying identity on $R.H.S.$ we get,
$(a-b)^{3}=a^{3}-b^{3}-3 a^{2} b+3 a b^{2}$
$\Rightarrow x^{3}-4 x^{2}-x+1=x^{3}-8-6 x^{2}+12 x$
$\Rightarrow x^{3}-4 x^{2}-x+1-x^{3}+8+6 x^{2}-12 x=0$
$\Rightarrow 2 x^{2}-13 x+9=0$
Degree of the equation is $2$ and
It is of the form $a x^{2}+b x+c=0,$ with $a \neq 0$ , therefore, the given equation is quadratic.
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