Question

2 more than the difference of a square of a number and the number gives a second number. The sum of the two numbers is 6. Find the two numbers

Answer 1

Let n be the number and y the second number.

x^2 - x + 2 = y
x + y = 6
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Answer 2

x^2 - x + 2 = y

x + y = 6 ---> y = 6 - x

In the first equation, in place of y substitute 6 - x which is what y equals in the second equation


x^2 - x + 2 = 6 - x

Add x to both sides

x^2 + 2 = 6

x ^ 2 = 4

Solve for x. There will be two values.

Then, use y = 6 - x to find the y value that goes with each one of the two y values.

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