Question #44605

1 Answer
Mar 9, 2016

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#