Answer:
There are two solutions for [tex]b[/tex]: [tex]b = + 30\cdot z[/tex], [tex]b = -30\cdot z[/tex]
Step-by-step explanation:
By Algebra, we know that a polynomial is a perfect square trinomial if it is of the form:
[tex]a^{2} + 2\cdot a \cdot c + c^{2} = (a + c)^{2}[/tex] (1)
By direct comparison, we have the following system:
[tex]a^{2} = 25\cdot z^{2}[/tex], [tex]c^{2} = 36[/tex], [tex]2\cdot a \cdot c = b[/tex].
There are two possible solutions for [tex]b[/tex]:
1) [tex]a = \pm 5\cdot z[/tex], [tex]c = \pm 6[/tex], [tex]b = + 30\cdot z[/tex]
2) [tex]a = \pm 5\cdot z[/tex], [tex]c = \mp 6[/tex], [tex]b = -30\cdot z[/tex]
