Answer:
The greatest possible value is 54
Step-by-step explanation:
Solve the quadratic equation
Given
x² - 5mx + 6m² = 0
We can rewrite this as
x² - 3mx - 2mx + 6m² = 0
(x² - 3mx) - (2mx - 6m²) = 0
x(x - 3m) - 2m(x - 3m) = 0
(x - 2m)(x - 3m) = 0
x - 2m = 0 or x - 3m = 0
So,
x = 2m or x = 3m .
2m and 3m are the roots of the equation.
Since one of the roots is 36
Assume
2m = 36
m = 36/2 = 18
3m is
3(18) = 54
If 3m = 36
m = 12
And
2m = 2(12) = 24.
The greatest possible value is 54
