Respuesta :
Answer:
26
Step-by-step explanation:
Question says that 'a' and 'b' are integers that implies we cannot have 'a' and 'b' in the form of decimals.
Now, lets expand the given equation:
[tex]a^2-b^2=100[/tex]
[tex](a+b)(a-b)=100[/tex]
Lets say: [tex](a+b)=p[/tex], [tex](a-b)=q[/tex]
Let us consider the factor pairs of 100.
[tex](1 \times 100), (2 \times 50), (4 \times 25), (5 \times 20), (10 \times 10), (20 \times 5), (25 \times 4), (50 \times 2), (100 \times 1)[/tex]
Only factor pair [tex](2,50)[/tex] gives us the integer values of 'a' and 'b'.
[tex]a+b=50[/tex]....equation (1)
[tex]a-b=2[/tex]........ equation (2)
adding equation 1 and 2, we get:
[tex]2a=52[/tex]
[tex]a=\frac{52}{2}=26[/tex]
[tex]a-b=2[/tex]
Plugging the value of 'a' in the equation 2
[tex]26-b=2[/tex]
[tex]b=24[/tex]
So the greatest possible value of 'a' is 26.
