Question

Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?

Answer 1

see explanation

Explanation:

`(5)/(x)` -
`(2)/(x^2)` = 2

multiply through by x² ( x ≠ 0 ) to clear the fractions

5x - 2 = 2x² , that is

2x² = 5x - 2 ( subtract 5x - 2 from both sides )

2x² - 5x + 2 = 0 ← in standard form

(2x - 1)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

x - 2 = 0 ⇒ x = 2

since x₁ < x₂ , then

x₁ =
`(1)/(2)` and x₂ = 2

Then

3x₁ + x₂

= 3 ×
`(1)/(2)` + 2

=
`(3)/(2)` + 2

=
`(3)/(2)` +
`(4)/(2)`

=
`(7)/(2)`