Factorize $4x^4 - 25x^2 + 36$.

Given: $4x^4 - 25x^2 + 36$.

To do: To factorize.

Solution:

One of the simplest way that know is:

Let $x^2 = a$

Then equation is $4(x^2)^2–25x^2+36$

$\Rightarrow 4a^2–25a+36 = 0$

$\Rightarrow 4a^2-a(16+9)+36 = 0$

$\Rightarrow 4a^2–16a-9a+36 = 0$

$\Rightarrow 4a(a-4)-9(a-4) = 0$

$\Rightarrow (a-4) (4a-9) = 0$

Here,

$(a-4) = 0$ and $(4a-9) = 0$

$a = 4$ and $a = \frac{9}{4}$

First let $a = 4$

Then, $x^2 = \pm\sqrt{4}$

$x =\pm2$

Now let $a = \frac{9}{4}$

Then $\Rightarrow x^2 =\frac{9}{4}$

$\Rightarrow x^2 =\pm\sqrt{\frac{9}{4}}$

$\Rightarrow x =\pm\frac{3}{2}$

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Updated on: 10-Oct-2022

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