Mathematics: If a and b are integers such that a2 − b2 = 100, what is the greatest possible value of a?

I figured out the answer Chaseashley24! The answer to your question is:0.673 m/s²Hope this helps!...

If a and b are integers such that a2 − b2 = 100,

kayla942783

11.03.2022

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:

a^2-b^2=100

(a+b)(a-b)=100

Lets say: (a+b)=p , (a-b)=q

Let us consider the factor pairs of 100.

$(1 \times 100), (2 \times 50), (4 \times 25), (5 \times 20), (10 \times 10), (20 \times 5), (25 \times 4), (50 \times 2), (100 \times 1)$

Only factor pair (2,50) gives us the integer values of 'a' and 'b'.

a+b=50 ....equation (1)

a-b=2 ........ equation (2)

adding equation 1 and 2, we get:

2a=52

$a=\frac{52}{2}=26$

a-b=2

Plugging the value of 'a' in the equation 2

26-b=2

b=24

So the greatest possible value of 'a' is 26.

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