Difference of two number

The difference of two numbers is 20. They are positive integers greater than zero. The first number raised to one-half equals the second number. Determine the two numbers.

Correct result:

a =  25
b =  5

Solution:

$$\begin{gathered} a-b=20 \\ {b}^2=a=25=0 \\ {b}^2-b-20=0 \\ {b}^2-b-20=0 \\ {b}^2-b-20=0 \\ p=1;q=-1;r=-20 \\ D=q^2-4pr=1^2-4\cdot 1\cdot (-20)=81 \\ D>0 \\ {b}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{1\pm \sqrt{81}}{2}} \\ {b}_{1,2}={\displaystyle \frac{1\pm 9}{2}} \\ {b}_{1,2}=0.5\pm 4.5 \\ {b}_1=5 \\ {b}_2=-4 \\ \text{ Factored form of the equation: } \\ (b-5)(b+4)=0 \\ b=b_1=5 \\ a=b^2=5^2=25 \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=b_1=5$

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