maths

the sum of a number and its square is one and a half times their difference. what is the number?

  1. 👍
  2. 👎
  3. 👁
  1. direct translation of the English to Math:

    x + x^2 = 1.5|x^2 - x|

    case1:
    times 2
    2x + 2x^2 = 3x^2 - 3x
    x^2 - 5x = 0
    x(x-5) = 0
    x = 0 or x = 5

    or

    case2:
    x+x^2 = 1.5(x-x^2)
    times 2
    2x + 2x^2 = 3x - 3x^2
    5x^2 - x = 0
    x(5x-1) = 0
    x = 0 or x = 1/5

    so x = 0 , (the trivial case)
    or x = 5 or x = 1/5

    check:
    the x = 0 case we can check mentally
    if x = 5
    sum of squares = 5 + 25 = 30
    their difference (25 - 5) = 20
    1.5 of that = 30 , check!

    if x = 1/5
    sum of squares = 1/5 + 1/25 = 6/25
    1.5(1/5 - 1/25) = 6/25 , check!

    x = 0, 5, 1/5

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Maths

    A two digit number is formed by either substracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits .find the number

  2. Math (Translate each sentance into a equation)

    1. The difference between three times a number and 11 is 10. Whould it be: 3x - 11 = 10? 2. One more than the difference between 18 and seven times a number is -9. Would it be: 1 + 18 - 7x = -9? 3. 26 more than the product of a

  3. Math please help with these word problems i have

    1. The circumference of a circle is the product of the number π and twice the radius. 2. The area of a square is the square of the length of a side. 3. The perimeter of a square is four times the length of a side. 4. Force equals

  4. math

    If the digits of the number are reversed, the number is increased by 36. The sum of the digits in the number is two and one–half times their difference. What is the number?

  1. Mathmatics

    Prove algebraically that the difference between the square of any two consecutive integers is equal to the sum of these two integers. First number = n Second number = n+1 Square the second number: (?????)^2 Difference between the

  2. Algebra 1 Foundation Concepts rewrite

    1. Write an algebraic expression for the following word phrase: the quotient of r and 12. (1 point) A)r • 12 B)r + 12 C)r ÷ 12 F)r – 12 2. Write a word phrase for the algebraic expression 3x - 7. (1 point) A)the difference of

  3. Math

    Can anyone help me with these problems? 1. A square has a side of 2 decimeters. A new square is formed by joining the midpoints of the sides. If this procedure is repeated 6 times, what is the perimeter and area of the seventh

  4. mathematics

    the sum of the in a three digit number is 9. The tens digit is half the sum of the sum of the other two and the hundreds digit is half the units digit. Find the total value of the number.

  1. math

    the sum of a number and 3 times that number is 76. what is that number? PLEASE HELP ME I DON'T GET IT!!!!!!!! Mathematics is a language, so translate the English into "math" let the number be x "the sum of a number and 3 times

  2. Algebra

    The difference of two numbers is 12. The sum of the larger number and 3 times the smaller number is 20. Find the larger number.

  3. Simultaneous equation

    Ann is older than Betty. Their ages in years are such that twice the square of Betty's age subtracted from the square of Ann's age gives a number equal to 6 times the difference of their ages. Given also that the sum of their ages

  4. Math! Please Check My Answers

    Key: ☺ = My Answer! 2. Write a word phrase for the algebraic expression. 3x - 7 A. The difference of three times a number x and seven. B. The difference of seven and three times a number x. C. Three times a number x fewer than

You can view more similar questions or ask a new question.