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andre [41]
3 years ago
15

The square of a positive number is 24 more than 5 times a number. What is the value of the number?

Mathematics
2 answers:
romanna [79]3 years ago
7 0

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.


satela [25.4K]3 years ago
4 0
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!
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