6p^4 = p^2 + 2 trying to find out p?

Question

6p^4 = p^2 + 2 trying to find out p?

Answer 1

6p^4- p^2 -2=0

(3P^2 - 2 )( 2P^2 +1)=0

3p^2 -2 =0    or   2p^2 +1=0

3p^2= 2              2p^2 = -1

p^2 = 2/3              p^2 = -1/2

p= sq rt (2/3)         p = sqrt (-1/2)

p= (sq rt 6)/3         p= i (sqrt 2)/2    if you use complex numbers

Answer 2

6p^4-p^2-2=0

3p^2-2  2p^2+1

3p^2=2

p^2=2/3

p= sqrt 2/3 or

2p^2=-1

p^2=-1

p = i

Answer 3

6p^4 - p^2 - 2 = 0

This equation is actually a quadratic hiding in an odd form.

Substitute x for p^2 and you see

6x^2 - x - 2 = 0

Factor to get

(3x - 2)(2x + 1) = 0

By the zero property...

x = 2/3 or x = -1/2

But, x = p^2

so...

p^2 = 2/3

or

p^2 = -1/2

Assuming you are working with the real numbers, ignore "p^2 = -1/2" as a square can't be negative.

So,

p^2 = 2/3

p = sqrt(2/3) or p = -sqrt(2/3)

Plug these values back into the original to check

6*((sqrt(2/3))^4) = (sqrt(2/3))^2 + 2

6*(2/3)^2 = 2/3 + 2

6*4/9 = 2/3 + 2

24/9 = 6/9 + 18/9

24/9 = 24/9 CHECK

6*((-sqrt(2/3))^4) = (-sqrt(2/3))^2 + 2

6*(2/3)^2 = 2/3 + 2

6*4/9 = 2/3 + 2

24/9 = 6/9 + 18/9

24/9 = 24/9 CHECK

So the answers are correct...

p = sqrt(2/3) or p = -sqrt(2/3)

Answer 4

6p^4 = p² + 2 => 6p^4 - p² - 2 = 0 =>  6p^4 + 3p² - 4p² - 2 = 0

3p²(2p² + 1) -2(2p² + 1) = 0 => (3p² -2)(2p² + 1) = 0

Hence p² = 2/3 or p² = -½ (This may be ignored, as the roots will be imaginary)

p = ±Sqrt(2/3)

AJM

Answer 5

p = 1 / square root of 3

Answer 6

Just let x be equal to p^2

so

6x^2=x+2

6x^2 -x -2

By factoring

(3x-2)(2x+1)

3x=2         2x=-1

x=2/3        x=-1/2

Replacing x by p^2

p^2=2/3              

p=sqrt(2/3)

reject the x=-1/2 since you can get the sqrt of a negative number

so p=sqrt(2/3)

Answer 7

you can solve this by factorising it.

(3p^2-2)(2p^2+1)=0

that is,3p^2=2

neglect the other value because it is imaginary.

that is,p^2=(2/3)

or,p=sqrt(2/3)

Answer 8

  6p^4-p^2 -2=0.

   6p^4 -4p^2 +3p^2 -2=0.

2p^2 ( 3p^2 -2) +1 ( 3p^2 -2)=0.

  (2p^2 +1) ( 3p^2 -2)=0.

  2p^2 +1=0, 2p^2= -1, p^2 = -1/2.

  3p^2 -2=0. 3p^2 =2, p^2= 2/3. p= sq root of +or - (2/3).