How do you solve #x^ { 4} - 51x ^ { 2} = - 50#?

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Answer 1 · 2016-12-26T02:57:18

We need to first equate this equation to #0# while keeping the equation balanced:

Answer 2 · 2016-12-26T04:12:43

#x=-sqrt50# or #sqrt50# or #-1# or #1#.

#x^4-51x^2=-50# can be written as #x^4-51x^2+50=0#

or #x^4-50x^2-x^2+50=0#

or #x^2(x^2-50)-1(x^2-50)=0#

or #(x^2-50)(x^2-1)=0# and using identity #(a^2-b^2)=(a+b)(a-b)#

or #(x+sqrt50)(x-sqrt50)(x+1)(x-1)=0#

i.e. either #x+sqrt50=0# or #x-sqrt50=0# or #x+1=0# or #x-1=0#

i.e. #x=-sqrt50# or #sqrt50# or #-1# or #1#.