Question

The square of a number plus the number is 72. Find the number(s)

Answer 1

The answer would be 8, 8 times 8 is 64 plus 8 is 72

Answer 2

Answer: x = 64[/tex]

Step-by-step explanation:

In mathematical notation, the problem is to solve the following equation

$\sqrt{x} + x = 72$

We can assume that the new variable is $(x^{1/2})$, so the equation is:

$(x^{1/2} )^{2} + (x^{1/2} ) -72 = 0$

We can solve this like a normal quadratic equation

$x^{1/2} = \frac{-1±\sqrt{1-4(1)(-72)}}{2}$

$x^{1/2} = \frac{-1±17}{2}$,

The solutions are

$x^{1/2} = -9 \\ x^{1/2} = 8$

We use the positive one, because a square can not be negative

So, $x^{1/2} = 8, x = 64$

To prove the answer

$\sqrt{64} + 64 = 72$