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 b2=a=25=0 b2−b−20=0  b2−b−20=0 b2−b−20=0  p=1;q=−1;r=−20 D=q2−4pr=12−4⋅1⋅(−20)=81 D>0  b1,2=−q±D2p=1±812 b1,2=1±92 b1,2=0.5±4.5 b1=5 b2=−4   Factored form of the equation:  (b−5)(b+4)=0 b=b1=5 a=b2=52=25a-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=b1=5

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  • Stones 3
    stones Simiyu and Nasike each collected a number of stones in an arithmetic lesson. If Simiyu gave Nasike 5 stones, Nasike would have twice as many stones as Simiyu. If initially, Simiyu had five stones less than Nasike how many stones did each have?
  • The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  • Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  • Children
    children_3 The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
  • Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  • Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160
  • Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
  • Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  • Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  • Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  • Men, women and children
    regiojet On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
  • Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  • Guppies for sale
    guppies Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Nancy
  • Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.