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). [tex]x^{2}+\frac{1}{2}x+a^2[/tex]
[tex]x^{2}+2(\frac{1}{4})x+a^2[/tex]
To make this expression a perfect square,
a² = [tex](\frac{1}{4})^2[/tex]
[tex]x^{2}+2(\frac{1}{4})x+(\frac{1}{4})^2[/tex] = [tex](x+\frac{1}{4})^2[/tex]
Therefore, the missing number will be [tex]\frac{1}{16}[/tex].
