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For what non-zero value of x,
[tex]p^4 - 2p^2x^2 + x^4 + x[/tex]
will be a perfect square?
[tex]a) \frac{1}{4p} \\ b)4p \\ c) {4p}^{2} \\ d) \frac{1}{ {4p}^{2} } [/tex]
I need step-by-step explanation. No spam. Thank you in anticipation.

Respuesta :

mhanifa

Answer:

  • d) 1/(4p²)

Step-by-step explanation:

Let's complete the square first:

  • p⁴ - 2p²x² + x⁴ + x =
  • p⁴ + 2p²x² + x⁴ - 4p²x² + x =
  • (p² + x²)² - (4p²x² - x)

In order the expression above to be a perfect square, we need:

  • 4p²x² - x = 0

Solve it for x:

  • 4p²x² = x
  • 4p²x = 1
  • x = 1/(4p²)

Correct choice is d

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