First, let's turn all the numbers into improper fractions so that we can find the answer easier.
-2 = r -
- = r -
Now we have to isolate 'r'.
First, we have to make sure that the variable is on one side and all the numbers are on the other side.
To do this, we have to add to both sides.
In order to do this, we need to ensure that both fractions have a common denominator.
- = r -
Ensure that the denominators are the same:
= r -
+
= r
= r
Good luck!
Answer:
Γ = 15
Step-by-step explanation:
Given
f(x) = x² - 8x + Γ
with a = 1, b = - 8 and c = Γ , then
sum of zeros α + β = - = -
= 8
product of zeros = αβ = = Γ
Given α - β = 2 , then
(α - β)² = 2²
α² - 2αβ + β² = 4 → (1)
and
(α + β)² = 8²
α² + 2αβ + β² = 64 → (2)
Add (1) and (2) term by term
2α² + 2β² = 68 ( divide through by 2 )
α² +β² = 34
Substitute α² + β² = 34 into (1)
34 - 2αβ = 4 ( subtract 34 from both sides )
- 2αβ = - 30 ( divide both sides by - 2 )
αβ = 15
Now
αβ = Γ = 15
Thus
f(x) = x² - 8x + 15