Let's go through the steps thoroughly to identify the error.
We start from the Pythagorean theorem applied to the sides given:
1. [tex]\(B A = \sqrt{1 + d^2}\)[/tex]
2. [tex]\(B C = \sqrt{e^2 + 1}\)[/tex]
3. [tex]\(C A = d - e\)[/tex]
Step 7 applies the Pythagorean theorem:
[tex]\[
\left(\sqrt{1+d^2}\right)^2 + \left(\sqrt{e^2 + 1}\right)^2 = (d - e)^2
\][/tex]
Simplifying this, we get:
[tex]\[
(1 + d^2) + (e^2 + 1) = (d - e)^2
\][/tex]
Combining the terms on the left-hand side, we have:
[tex]\[
1 + d^2 + e^2 + 1 = d^2 - 2de + e^2
\][/tex]
[tex]\[
2 + d^2 + e^2 = d^2 - 2de + e^2
\][/tex]
Subtracting [tex]\(d^2 + e^2\)[/tex] from both sides:
[tex]\[
2 = -2de
\][/tex]
Dividing by -2:
[tex]\[
-1 = de
\][/tex]
Therefore, step 8 seems to be logically correct based on our simplifications. However, let’s check if these simplifications hold correctly.
The equation [tex]\(d^2 - 2de + e^2\)[/tex] on the right side is obtained from [tex]\((d - e)^2\)[/tex].
The equation [tex]\(2 = -2de\)[/tex] is obtained by removing [tex]\(d^2 + e^2\)[/tex] from both sides, as:
[tex]\[
2 = -2de
\][/tex]
and
[tex]\(-1 = de\)[/tex].
Hence, there are no errors in steps 7 and 8 directly based on the operations carried out.
Revisiting the given table:
[tex]\(
BC = \sqrt{e^2 + 1}
\)[/tex]
[tex]\(
CA = d - e
\)[/tex] should rather be:
[tex]\(
CA = \sqrt{(d - e)^2}
\)[/tex]
Finally verifying each,
We return to the initial decimal assumption rooted in:
Step 6 [tex]\(\sqrt{\left(d - e^2\right)} = d - e\)[/tex] preliminary.
If mistaken simplification, \(C = \sqrt{d - e^2},
Correct:
(d - e)^2 mismatch equating\(√ (( mismatch to).
which
Thus error cause redirect established implies in Step 8
Thus;\ careful confirm error initial step identically thus step mistake step 7.
- So Answer:
- A
- Step 6.
