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Beatles11

First, let's construct an algebraic equation to formally find the answer:

Let x represent (the value of) the unknown number. 

x²= 5x + 24 --- This equation shows that the (positive) number's square equals 24 more than 5 times the number.

Now we can solve for x (the number):

                 x² = 5x + 24
  x² - 5x - 24 = 0
(x + 3)(x - 8) = 0
                   x =  -3, 8

Therefore, this means that x (the number ) can be either -3 OR 8. Both will satisfy the description.
Hope this helps!

Answer:  The positive number is \(8\).


Step-by-step explanation: Let, the positive number to find be \(x\). Then, its square will be \(x^{2}\). Sicne \(x^2\) is \(24\) more than \(5x\), so, while forming an algebraic equation from the given information, we will write

\(x^{2} -24=5x\\\Rightarrow x^{2} -5x-24=0\\\Rightarrow x^{2} -8x+3x-24=0\\\Rightarrow x(x-8)+3(x-8)=0\\\Rightarrow (x-8)(x+3)=0,\)

which gives

\(x-8=0\Rightarrow x=8\)

and

\(x+3=0\Rightarrow x=-3.\)

Since the given number is positive, so \(x=-3\) cannot be true. Hence, \(x=8\) is the solution.

Thus, the positive number is \(8\).


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