How do you solve #x^4 - 2x^2 - 8 = 0#?
3 Answers
you should ask yourself what two numbers do you multiply to get -8 and their summation is -2
and that is -4 and +2 so
Explanation:
#"make the substitution "u=x^2#
#rArru^2-2u-8=0#
#"the factors of - 8 which sum to - 2 are - 4 and + 2"#
#rArr(u-4)(u+2)=0#
#"equate each factor to zero and solve for u"#
#u-4=0rArru=4#
#u+2=0rArru=-2#
#"change u back into terms of x"#
#u=4rArrx^2=4rArrx=+-2#
#u=-2rArrx^2=-2rArrx=+-sqrt2i#
If x is not explicitly real,
Explanation:
Substitute
This is just to make it look less intimidating to factor
Factor:
Substitute back:
Factor:
If you weren't taught imaginary numbers yet, skip the rest of this, you don't need it: