Question

Question #44605

Answer 1

It has not been stated explicitly what is required to be done. Assuming that we are required to find all four roots of the equation, these are: `x=+-1, +-sqrt7`

Explanation:

Given equation is
`x^4-8x^2+7=0`......(1)
Let's assume that
`x^2=y`, on substitution the equation becomes
`y^2-8y+7=0` .......(2)
Lets use the split the middle term method. Two parts of middle term whose product is equal to the product of first and third terms which is `(y^2)(7)=7y^2`

On inspection we find twp parts as `-7y and -y`
Equation can be rewritten as
`y^2-y-7y+7=0`
Taking `y` common out first two terms and `7` out of last two we obtain
`y(y-1)-7(y-1)=0`
Again taking `(y-1)` common out of two terms we obtain
`(y-1)(y-7)=0`
To find the roots set each term equal to zero.
`:. (y-1)=0 and (y-7)=0`
First gives us

`y=1` and from the second we get
`y=7`. Putting in the value of `x` in terms of `y` as assumed we obtain
`x^2=1=>x=+-1` and
`x^2=7=>x=+-sqrt7`