# maths

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

1. 👍 0
2. 👎 0
3. 👁 656
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. 👍 0
2. 👎 0
2. ?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

Write an inequality and solve. Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four.

2. ### math

write each expression using n as your variable.then simplify fully. 1.five more than the sum of a number and ten. 2.the product of eight and seven less than a number. 3.the quotient of a number and three, increased by one. 4.ten

3. ### 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

4. ### 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

1. ### 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

2. ### 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?

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

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

1. ### algebra

One number is 4 times another. If the sum of their reciprocals is 5/36 , find the two numbers. I am total lost on this problem x is a number 4x is another number these should = 5/36 so my equation would be x+4x=5/36 first x i am

2. ### Arithmetic Progression

In an AP the 6th term is half the 4th term and the 3rd term is 15. a. Find the fist term and the common difference. b. How many times are needed to give a sum that is less than 65?

3. ### Mathematics

I need help writing algebraic expressions into equations 1) the product of a number and 7 is 63 2) 10 subtracted from a number is 15 3) two-fifths of a number is -12 4) 8% of a number is 20 5) the sum of twice a number and 17 is

4. ### math

negative one times the sum of twice a number and 3 is equal to two times the difference of -4 times the number and 3. what is the number?