Let's simplify the given expression step-by-step to understand the process fully.
We have the expression:
[tex]\[
\frac{4.5 \times 4.5 - 1.4 \times 1.4}{3.5 - 1.4}
\][/tex]
### Step 1: Calculate the Numerator
First, we need to calculate each part of the numerator separately:
1. Calculate [tex]\(4.5 \times 4.5\)[/tex]:
[tex]\[
4.5 \times 4.5 = 20.25
\][/tex]
2. Calculate [tex]\(1.4 \times 1.4\)[/tex]:
[tex]\[
1.4 \times 1.4 = 1.96
\][/tex]
3. Subtract the second value from the first:
[tex]\[
20.25 - 1.96 = 18.29
\][/tex]
So, the numerator is [tex]\(18.29\)[/tex].
### Step 2: Calculate the Denominator
Next, we'll calculate the denominator:
1. Subtract [tex]\(1.4\)[/tex] from [tex]\(3.5\)[/tex]:
[tex]\[
3.5 - 1.4 = 2.1
\][/tex]
So, the denominator is [tex]\(2.1\)[/tex].
### Step 3: Simplify the Expression
Now we divide the numerator by the denominator:
[tex]\[
\frac{18.29}{2.1} \approx 8.71
\][/tex]
Thus, the simplified value of the given expression is approximately [tex]\(8.71\)[/tex].
### Conclusion
There is no answer option exactly matching [tex]\(8.71\)[/tex] from the given choices:
(a) 3.1,
(b) 5.9,
(c) 4.1
Therefore, none of the provided options (a), (b), or (c) are correct. The correct simplified value should be approximately [tex]\(8.71\)[/tex].
