Adding 42 to a given positive number gives the same result as squaring the number. Find the number
Answer Details
Let's call the unknown number "x".
According to the problem, adding 42 to x gives the same result as squaring x. We can write this as an equation:
x + 42 = x^2
To solve for x, we can rearrange this equation to get it in standard quadratic form:
x^2 - x - 42 = 0
Now we can factor this quadratic equation:
(x - 7)(x + 6) = 0
This gives us two possible solutions: x = 7 and x = -6. However, we were given that x is a positive number, so we can discard the negative solution. Therefore, the answer is x = 7.
To check our answer, we can substitute x = 7 into the original equation:
7 + 42 = 49
7^2 = 49
So adding 42 to 7 does indeed give the same result as squaring 7.