Solve the following equations, $6 x^{4} - 13 x^{3} + 12 x^{2} - 13 x + 6 = 0$

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Solution

we can write it as

$(6 x^{4} + 12 x^{2} + 6) - (13 x^{3} + 13 x)$

= $6 (x^{2} + 1)^{2}$ - $13 x (x^{2} + 1)$

= $(x^{2} + 1) (6 x^{2} - 13 x + 6) = 0$

$∴$ $x =$ $\frac{2}{3}$ , $\frac{3}{2}$

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