Question

Solve x4 – 17x2 + 16 = 0.

Answer 1

Answer:

x=+4. -4. +1, -1

Step-by-step explanation:

In order to solve this you just need to factorize the different possibilites of the equation, you need to search for two numbers that added up would sum -17 and multiplied would be +16, so we can come up with the next numbers:

-16 and -1

So the factorization of the equation would be:

$(x^2-16)(x^2-1)=0$

Now you take each factor and equalize it to 0

$x^2-16=0\\x^2=16\\x=\sqrt{16} \\x= +4, -4$

$x^2-1=0\\x*2=1\\x=\sqrt{1} \\x= +1, -1$

So now you have the answer for the values that X can have and the equation to stil be true.

Answer 2

Solve for x over the real numbers:

x^4 - 17 x^2 + 16 = 0

Substitute y = x^2:

y^2 - 17 y + 16 = 0

The left hand side factors into a product with two terms:

(y - 16) (y - 1) = 0

Split into two equations:

y - 16 = 0 or y - 1 = 0

Add 16 to both sides:

y = 16 or y - 1 = 0

Substitute back for y = x^2:

x^2 = 16 or y - 1 = 0

Take the square root of both sides:

x = 4 or x = -4 or y - 1 = 0

Add 1 to both sides:

x = 4 or x = -4 or y = 1

Substitute back for y = x^2:

x = 4 or x = -4 or x^2 = 1

Take the square root of both sides:

Answer: x = 4 or x = -4 or x = 1 or x = -1

-Hope this helps-