Question

Enter the correct value so that each expression is a perfect square trinomial

Answer 1

Answer:

Step-by-step explanation:

1). x² - 10x + a²

  By using the formula of (a - b)² = a² - 2ab + b²

  x² - 2(5)x + a²

  Therefore, for a perfect square of the expression a should be equal to 5.

  Therefore, (x² - 10x + 25) will be the answer.

2). x² + 2ax + 36

  = x² + 2(a)x + 6²

  For a perfect square of the given expression value of a should be 6.

   x² + 2(a)x + 6² = x² + 2(6)x + 6²

                           = (x + 6)²

  Therefore, x² + 12x + 36 will be the answer.

3). $x^{2}+\frac{1}{2}x+a^2$

    $x^{2}+2(\frac{1}{4})x+a^2$

   To make this expression a perfect square,

   a² = $(\frac{1}{4})^2$

   $x^{2}+2(\frac{1}{4})x+(\frac{1}{4})^2$ = $(x+\frac{1}{4})^2$

  Therefore, the missing number will be $\frac{1}{16}$.