Please solve X^4-X^2-72=0?

Answer 1

Factor:

(x^2 - 9)(x^2 + 8) = 0

(x + 3)(x - 3)(x^2 + 8) = 0

Set Factors equal to zero and solve.

x + 3 = 0

x = -3

x - 3 = 0

x = 3

x^2 + 8 = 0

x^2 = -8

x = +/- SQRT (-8)

x = +/- 2i SQRT (2)

So, this equation has two real solutions 3 and -3 and two imaginary solutions 2i SQRT (2) and -2i SQRT (2)

Answer 2

a) sparkling up with the aid of factorising x2 - 6x + 8 = 0 wreck up the 8 into its factors, and then perceive 2 which upload to furnish -6 and multiply to furnish 8. you will desire to get -2 and -4. subsequently, (x-2)(x-4) = 0 --- ab = 0, a=0 or b=0 x= 2 or 4. --------------------------- b) sparkling up employing the quadratic formula. x= [-b±?(b2 - 4ac)] / 2a in x2 - 6x + 8 = 0, a = a million, b = -6 and c = 8 x = [6±?(36-32)] / 2 x = [6±2]/2 x = 2 or 4 --------------------------- 2) For the function y = x2 - 6x + 8, carry out here projects: a) positioned the function in the style y = a(x - h)2 + ok. This includes ending up the sq.. y = x2 - 6x + 8 y = x2 - 6x + 9 - a million y = (x-3)2-a million ---------------------------- b) what's the equation for the line of symmetry for the graph of this function? From section (a), the equation for the line of symmetry is x=h, subsequently x = 3 ---------------------------- c) [Graph] this is not had to devise factors, as you will locate the equation of the line of symmetry, the vertex or turning element and intercepts very actual. ---------------------------- d) The graph has the comparable shape, yet is shifted a million unit down, and 3 gadgets to the excellent. ---------------------------- 3) you're given the final equation and all the variables, so in basic terms pop them in and you get: s = -16t2 + 32t --------------------------- b) Sub in t=a million, s = -sixteen(a million)2+32(a million) = 16ft. --------------------------- c) while it hits the floor, the s = 0. 0 = -16t2 + 32t 0 = t2 - 2t 0 = t(t-2) t = 0 or 2 seconds. Discarding the 0 answer, we get t = 2 seconds. ---------------------------- d) the optimal top is midway between launch and hitting the floor, at t = a million 2d. you ought to use the respond from b, 16ft. ----------------------------------- 4) The equation for the fringe is: 2(l+w) = 400ft. l + w = 200ft. l = 2 hundred - w. The equation for the section is A = l x w. sub in (2 hundred-w) for l, A = w(2 hundred-w) A = - w2 + 200w we would desire to constantly locate the turning (optimal) element. The equation for the line of symmetry is -b/2a = -2 hundred/-2 = a hundred subsequently on the max, w = 100ft and l = 2 hundred-a hundred = 100ft. the section right this is 10,000 ft2.

Answer 3

The standard scheme is:

Let t = x^2, t > 0
X^4-X^2-72=0
=> t^2 - t - 72 = 0
=> quadratic equation of t

Delta = 1 - 4*(-72) = 1+288 = 289 = 17^2

t1 = [1 + sqrt(17^2)]/2 = (1+17)/2 = 9
t2 = [1 - sqrt(17^2)]/2 = (1-17)/2 = -8 <0 => not accepted.


then in total, there are two solutions:

x1 = sqrt(9) = 3
x2 = - sqrt(9) = -3

Answer 4

X = 3

3^4 = 81
3^2 = 9

81 - 9 = 72

72 - 72 = 0 YES!

Answer 5

X^4-X^2-72=0
There will be four answers.

(x^2-9)(x^2+8) = 0
(x+3)(x-3)(x^2+8) = 0
x+3 = 0; so x = -3
x-3 = 0; so x = 3
x^2 = -8; so x = 2i*sqrt2 or -2i*sqrt2

Answer 6

Factor as much as we can.
(x^2 + 8)(x^2 - 9) = 0
(x^2 + 8)(x + 3)(x - 3) = 0

Now we can solve for x

The first term:
Subtract 8 from both sides
x^2 = -8
This has an imaginary solution.
x = 2i(2^0.5) and -2i(2^0.5)

Now the second two terms
(x + 3)(x - 3) = 0
x= -3 and x = 3

All four solutions from above are

x = 2i(2^0.5), x = -2i(2^0.5), x= -3, x = 3
.

Answer 7

x^4 - x^2 - 72 = 0
(x^2 - 9)(x^2 + 8) = 0
X^2 - 9 = 0 or x^2 + 8 = 0
X = sqrt 9 x= sqrt 8
X = 3 or -3

That's it!

Answer 8

x^4-9x^2+8x^2-72=0

x^2(x^2-9)+8(x^2-9)=0

(x^2-9)(x^2+8)=0

x=(+/-)3,(+/-)i2*sq rt(2) where i=sq rt(-1)