Sure, let's break the problem down step-by-step to see how we arrived at the value for [tex]\( a - b \)[/tex].
We are given:
- [tex]\( a + b = 50 \)[/tex]
- [tex]\( ab = 400 \)[/tex]
We need to find [tex]\( a - b \)[/tex].
To achieve this, we can use the formula:
[tex]\[ a - b = \sqrt{(a + b)^2 - 4ab} \][/tex]
Let's substitute the given values into the formula:
1. Plug in [tex]\( a + b \)[/tex] and [tex]\( ab \)[/tex]:
[tex]\[
a - b = \sqrt{(50)^2 - 4 \cdot 400}
\][/tex]
2. Compute the square and product:
[tex]\[
a - b = \sqrt{2500 - 1600}
\][/tex]
3. Subtract the quantities under the square root:
[tex]\[
a - b = \sqrt{900}
\][/tex]
4. Take the square root of the remaining value:
[tex]\[
a - b = \sqrt{30^2}
\][/tex]
5. Simplify the square root to get the final result:
[tex]\[
a - b = 30
\][/tex]
Thus, [tex]\( a - b = 30 \)[/tex].
