Let's break it down step by step to solve for [tex]\( R \)[/tex] and [tex]\( S \)[/tex], and then compute [tex]\( R^2 + S^2 \)[/tex].
1. Given:
- [tex]\( P = 10 \)[/tex]
- [tex]\( H = 2 \)[/tex]
- [tex]\( Q = 5 \)[/tex]
2. Calculate [tex]\( R \)[/tex]:
[tex]\[
R = P \cdot H \cdot Q
\][/tex]
[tex]\[
R = 10 \cdot 2 \cdot 5
\][/tex]
[tex]\[
R = 100
\][/tex]
3. Calculate [tex]\( S \)[/tex]:
[tex]\[
S = P - Q
\][/tex]
[tex]\[
S = 10 - 5
\][/tex]
[tex]\[
S = 5
\][/tex]
4. Now, we need to find [tex]\( R^2 + S^2 \)[/tex]:
[tex]\[
R^2 = 100^2 = 10000
\][/tex]
[tex]\[
S^2 = 5^2 = 25
\][/tex]
[tex]\[
R^2 + S^2 = 10000 + 25 = 10025
\][/tex]
Therefore, the value of [tex]\( R^2 + S^2 \)[/tex] is [tex]\( 10025 \)[/tex]. This is the final result.
