# 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:

$a-b=20 \ \\ b^2=a=25=0 \ \\ b^2-b-20=0 \ \\ \ \\ b^2-b-20=0 \ \\ b^2 -b -20=0 \ \\ \ \\ p=1; q=-1; r=-20 \ \\ D=q^2 - 4pr=1^2 - 4\cdot 1 \cdot (-20)=81 \ \\ D>0 \ \\ \ \\ b_{1,2}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 1 \pm \sqrt{ 81 } }{ 2 } \ \\ b_{1,2}=\dfrac{ 1 \pm 9 }{ 2 } \ \\ b_{1,2}=0.5 \pm 4.5 \ \\ b_{1}=5 \ \\ b_{2}=-4 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (b -5) (b +4)=0 \ \\ b=b_{1}=5 \ \\ a=b^2=5^2=25$

Checkout calculation with our calculator of quadratic equations.

$b={b}_{1}=5$

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