SOLUTION: x^4+(sqrt 76)x^2-76=0

Question 753021: x^4+(sqrt 76)x^2-76=0
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Giving you some tricky questions are they? I think we can handle it. It just a little complicated on-line.
First, to reduce the order of the polynomial, let
(1) y = x^2, then your equation reduces to
(2) y^2 + sqrt(76)*y -76 = 0
Now use the quadratic equation to find the roots of (2).
(3) y = or
(4) y = or
(5) y = or
(6) y =
Since y = x^2 we get
(7) x = +/-sqrt(y) and since y has two roots we will get four roots for x.
Taking the square root of (6) gives us two roots of x
(8) and
(9)
Likewise we can write the other two roots of x as
(10) and
(11)
We acn check these roots by substitution into your original equation in x. I'll use x of (8) to show that
(12)
We have
(13) and
(14)
Now put (13) and (14) into (12) and get
(15) or
(16)
Multiply (16) by 4/76 and get
(17) or
(18) or
(19) or
(20) or
(21) or
(22) 0 = 0 check
Answers: the roots of your quardic equation are given by (8)-(11)

RELATED QUESTIONS
76-4(x+9)=0 (answered by jim_thompson5910)

4.6^x-76=0 (answered by jsmallt9)

4.6^x-76=0 (answered by edjones)

How do I finish this? x^2+8x-3=0 x^2+8x=3 x^2+8x+64/4=3/1+64/4=12/4+64/4=76/4... (answered by rchill)

(76-40 x 2) + (2 x... (answered by stfuenaira)

76 =... (answered by Alan3354)

9x/(5-x)=76 (answered by checkley79)

Hi, I'm studying for a test and the problem below seems so simple, but I can't figure... (answered by scott8148)

x^2+y^2=76 x^2-y^2=4 What are all the possible... (answered by josgarithmetic)