Question

The sum of a number and its square is 1 and half times their difference. Find the number​

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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

Method 1

times 2

2x + 2x^2 = 3x^2 - 3x

x^2 - 5x = 0

x(x-5) = 0

x = 0 or x = 5

or

Method 2

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

Hope it helps you mate