Respuesta :
For this case we will solve the equations step by step:
a2 - 9a + 14 = 0
(a-7) * (a-2) = 0
a1 = 7
a2 = 2
{7, 2}
a2 + 9a + 14 = 0
(a + 7) * (a + 2) = 0
a1 = -7
a2 = -2
{-2, -7}
a2 + 5a - 14 = 0
(a + 7) * (a-2) = 0
a1 = -7
a2 = 2
{2, -7}
a2 - 5a - 14 = 0
(a-7) * (a + 2) = 0
a1 = 7
a2 = -2
{-2, 7}
a2 - 9a + 14 = 0
(a-7) * (a-2) = 0
a1 = 7
a2 = 2
{7, 2}
a2 + 9a + 14 = 0
(a + 7) * (a + 2) = 0
a1 = -7
a2 = -2
{-2, -7}
a2 + 5a - 14 = 0
(a + 7) * (a-2) = 0
a1 = -7
a2 = 2
{2, -7}
a2 - 5a - 14 = 0
(a-7) * (a + 2) = 0
a1 = 7
a2 = -2
{-2, 7}
Answer:
The solution set for the first equation is {2,7}.
The solution set for the second equation is {-2,-7}.
The solution set for the third equation is {-5,2}.
The solution set for the fourth equation is {2,-7}.
The solution set for the fifth equation is {-2,7}.
Step-by-step explanation:
The first equation is
[tex]a^2-9a+14=0[/tex]
[tex]a^2-7a-2a+14=0[/tex]
[tex]a(a-7)-2(a-7)=0[/tex]
[tex](a-7)(a-2)=0[/tex]
[tex]a-7=0\Rightarrow x=7[/tex]
[tex]a-2=0\Rightarrow x=2[/tex]
Therefore the solution set for the first equation is {2,7}.
The second equation is
[tex]a^2+9a+14=0[/tex]
[tex]a^2+7a+2a+14=0[/tex]
[tex]a(a+7)+2(a+7)=0[/tex]
[tex](a+7)(a+2)=0[/tex]
[tex]a+7=0\Rightarrow x=-7[/tex]
[tex]a+2=0\Rightarrow x=-2[/tex]
Therefore the solution set for the second equation is {-2,-7}.
The third equation is
[tex]a^2+3a-10=0[/tex]
[tex]a^2+5a-2a-10=0[/tex]
[tex]a(a+5)-2(a+5)=0[/tex]
[tex](a+5)(a-2)=0[/tex]
[tex]a+5=0\Rightarrow x=-5[/tex]
[tex]a-2=0\Rightarrow x=2[/tex]
Therefore the solution set for the third equation is {-5,2}.
The fourth equation is
[tex]a^2+5a-14=0[/tex]
[tex]a^2+7a-2a-14=0[/tex]
[tex]a(a+7)-2(a+7)=0[/tex]
[tex](a+7)(a-2)=0[/tex]
[tex]a+7=0\Rightarrow x=-7[/tex]
[tex]a-2=0\Rightarrow x=2[/tex]
Therefore the solution set for the fourth equation is {2,-7}.
The fifth equation is
[tex]a^2-5a-14=0[/tex]
[tex]a^2-7a+2a-14=0[/tex]
[tex]a(a-7)+2(a-7)=0[/tex]
[tex](a-7)(a+2)=0[/tex]
[tex]a-7=0\Rightarrow x=7[/tex]
[tex]a+2=0\Rightarrow x=-2[/tex]
Therefore the solution set for the fifth equation is {-2,7}.
