solve the below?

Question

(x^2-4x)^2-(x-4)^2-16=0

Answer 1

Are you sure this is copied correctly? It is close in some ways to what would be a quite elegant problem, but in its present form, it has to be multiplied out to get an unfactorable quartic equation and can only be solved numerically.

The TI-83 gives roots of

x1 = -2.565994563312
and
x2 = 4.8439519121702

Those are the ugly irrational roots to the problem you posed. Once again, are you sure this was copied correctly?

Answer 2

(x^2 - 4x)^2 - (x - 4)^2 - 16 = 0
x^4 - 8x^3 + 15x^2 + 8x - 32 = 0
(x - 4.843951913)(x + 1.256599458)
x^2 - 3.587352455x - 6.086907348)(x^2 + ax + 5.257185327) = x^4 - 8x^3 + 15x^2 + 8x - 32
- 3.587352455 + a = - 8
a = - 4.412647545
x^2 + - 4.412647545x = - 5.257185327
x^2 + - 4.412647545x + 4.867864589 = - 5.257185327 + 4.867864589

(x - 2.2063237725)^2 = - 0.3893207379

x - 2.2063237725 = ± j0.6239557179

x = 2.2063237725 - j0.6239557179
x = 2.2063237725 - j0.6239557179
x = 4.843951913
x = - 1.256599458

Answer 3

Simplify the given equation:
(taking x common from the first bracket)
x^2(x-4)^2-(x-4)-16=0
now put x-4 = t
thus x= t+4. substituting,
(t+4)^2 t^2 - t -16 = 0
opening the brackets ,
t^4 + 8t^3 + 16t^2 - t - 16 =0
this equation can be solved by polynomial solving of equations.(which i cant explain properly)

Answer 4

(x^2-4x)^2=x^4 - 2*x^2*4x + 16x^2= x^4 - 8x^3 + 16x^2
(x-4)^2 = x^2 - 2*x*4 - 4^2 = x^2 - 8x - 16
(x^2-4x)^2 - (x-4)^2 -16 = x^4 - 8x^3 + 16x^2 - ( x^2-8x-16) -16
= x^4 - 8x^3 + 16x^2 - x^2 + 8x + 16-16
=x^4 -8x^3 -15X^2 +8x

Answer 5

on expansion you will get ;
17x^2 - 16x^3 + 8x - 16 =0

Answer 6

What the **** know one well figure out that unless there smart enoth and I can't you shold've made an eiser one!