Solve `x^4 -13x^2 +36=0` `Thanks` ` `

zach2794 | Student

`x^4-13x^2+36=0`` `

We can split this up into:


Then with this being true we also know that

`(x^2-9)=0` and `(x^2-4)=0`

so solving for x we get that `x^2=9,4`

Taking the square root of both sides gives us:

Answer:`` `x=+-3,+-2`

llltkl | Student

Given `x^4-13x^2+36=0`

To solve for x, first factorize by splitting the middle term.  -13 can be written as the sum of 2 numbers which give a product 36. This can be done as -13 = -9 +(-4). So,


`rArr x^2(x^2-9)-4(x^2-9)=0`

`rArr (x^2-9)(x^2-4)=0`

`rArr {(x)^2-(3)^2}{(x)^2-(2)^2}=0`

Applying `a^2-b^2=(a+b)(a-b)` we get:


Therefore, x=-3,+3,-2,+2.

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