Question

The product of two rational numbers is 1.5. Their sum is 3.5. What are the two numbers?

Answer 1

The number are "x" and "y".
Then, we suggest this system of equations:
xy=1.5
x+y=3.5

we can solve this system of equations by substitution method.

y=3.5 - x

x(3.5-x)=1.5
3.5x-x²=1.5
x²-3.5x+1.5=0

We solve this square equation:

x=[3.5⁺₋√(12.25 - 6)] / 2=(3.5⁺₋2.5)/2

we have two solutions:
x₁=(3.5-2.5) / 2=0.5 then: y₁=3.5-x=3.5 - 0.5=3

x₂=(3.5+2.5)/2=3 then y₂=3.5-x=3.5-3=0.5

Therefore the two numbers are 3 and 0.5

Answer: the numbers are 3 and 0.5

Answer 2

easy, 3 and 0.5

but ok the math way

xy=1.5
x+y=3.5

y=3.5-x
x(3.5-x)=1.5
3.5x-x^2=1.5
0=x^2-3.5x+1.5
quadratic
ax^2+bx+c=0
x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}`

a=1
b=-3.5
c=1.5

x=
`\frac{-(-3.5)+/- \sqrt{(3.5)^(2)-4(1)(1.5)} }{2(1)}`
x=
`(3.5+/- √(12.25-6) )/(2)`
x=
`(3.5+/- √(6.25) )/(2)`
x=
`(3.5+/- 2.5)/(2)`
x=
`(3.5+ 2.5)/(2)` or x=
`(3.5- 2.5)/(2)`
x=6/2 or 1/2
x=3 or 0.5
those are the numbers


3 and 0.5