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Solve the following quadratic equation by factorization:
$9x^2\ β\ 6b^2x\ β\ (a^4\ β\ b^4)\ =\ 0$
Given:
Given quadratic equation is $9x^2\ –\ 6b^2x\ –\ (a^4\ –\ b^4)\ =\ 0$.
To do:
We have to solve the given quadratic equation by factorization.
Solution:
$9x^2\ –\ 6b^2x\ –\ (a^4\ –\ b^4)\ =\ 0$
$9x^2-6b^2x-(a^2-b^2)(a^2+b^2)=0$
$9x^2+3(a^2-b^2)x-3(a^2+b^2)x-(a^2-b^2)(a^2+b^2)=0$
$3x(3x+a^2-b^2)-(a^2+b^2)(3x+a^2-b^2)=0$
$(3x+a^2-b^2)(3x-a^2-b^2)=0$
$3x+a^2-b^2=0$ or $3x-a^2-b^2=0$
$3x=b^2-a^2$ or $3x=a^2+b^2$
$x=\frac{b^2-a^2}{3}$ or $x=\frac{a^2+b^2}{3}$
The roots of the given quadratic equation are $\frac{b^2-a^2}{3}$ and $\frac{a^2+b^2}{3}$.ββ
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