Nice answer Aziz....let's see how he might have gotten there......
Let x be the first number and y be the second ... so we have
x + y = 7.5
and
x * y = 9
Solving for y in the first equation, we have y = 7.5 - x
And substitutuing for y in the second equation
x * (7.5 - x) = 9 simplifying, we have
-x^2 + 7.5 x = 9 and rearranging, we have
x^2 - 7.5x + 9 = 0 subtract 9 from both sides
x^2 - 7.5x = -9 now, take 1/2 of the coefficient on x (= 3.75), square it (=14.0625) , and add the square to both sides...so we have
x^2 - 7.5x + 14.0625 = 5.0625 factor the left side
(x - 3.75)^2 = 5.0625 take the square root of both sides
x - 3.75 = ± 2.25
So x = 3.75 - 2.25 = 1.5 or x = 3.75 + 2.25 = 6
And whatever we choose as x, y is the other value, so Aziz's answer of 1.5 and 6 is correct!!!!
Nice answer Aziz....let's see how he might have gotten there......
Let x be the first number and y be the second ... so we have
x + y = 7.5
and
x * y = 9
Solving for y in the first equation, we have y = 7.5 - x
And substitutuing for y in the second equation
x * (7.5 - x) = 9 simplifying, we have
-x^2 + 7.5 x = 9 and rearranging, we have
x^2 - 7.5x + 9 = 0 subtract 9 from both sides
x^2 - 7.5x = -9 now, take 1/2 of the coefficient on x (= 3.75), square it (=14.0625) , and add the square to both sides...so we have
x^2 - 7.5x + 14.0625 = 5.0625 factor the left side
(x - 3.75)^2 = 5.0625 take the square root of both sides
x - 3.75 = ± 2.25
So x = 3.75 - 2.25 = 1.5 or x = 3.75 + 2.25 = 6
And whatever we choose as x, y is the other value, so Aziz's answer of 1.5 and 6 is correct!!!!