help please with solution
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Let x and y be the numbers you're looking for.
Given: xy = 1014
Given: x + y = 65
Rearrange that last one:
y = 65 - x
Substitute this value for y into the first given equation:
x (65 - x) = 1014
Expand:
65x - x^2 = 1014
Arrange in standard form:
x^2 - 65x + 1014 = 0
(I suspect this is the equation that caused your question in the first place.)
This time forget factoring and use the quadratic formula:
x = (65 ±√(4225 + 4056)) / 2 = (65 ± √169) / 2 = (65 ± 13) / 2
x = 26, 39
Substitute these values for x into y = 65 - x and solve for two values of y:
65 - 26 = 39
65 - 39 = 26
So the two numbers you want are 26 and 39.
Given: xy = 1014
Given: x + y = 65
Rearrange that last one:
y = 65 - x
Substitute this value for y into the first given equation:
x (65 - x) = 1014
Expand:
65x - x^2 = 1014
Arrange in standard form:
x^2 - 65x + 1014 = 0
(I suspect this is the equation that caused your question in the first place.)
This time forget factoring and use the quadratic formula:
x = (65 ±√(4225 + 4056)) / 2 = (65 ± √169) / 2 = (65 ± 13) / 2
x = 26, 39
Substitute these values for x into y = 65 - x and solve for two values of y:
65 - 26 = 39
65 - 39 = 26
So the two numbers you want are 26 and 39.
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26 + 39 = 65
26 x 39 = 1 014
26 x 39 = 1 014
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26 and 39