Solution:

Given equation: 2x2 + 3x + 7 = 0

Let α and β be the roots of the given equation.

We need to find the value of αβ-1 βα-1

Product of roots of the equation:

αβ = 7/2

Reciprocal of roots:

α-1 = β/7

β-1 = α/7

αβ-1 βα-1 = αβ(α-1)(β-1)

= 7/2 * (β/7) * (α/7)

= αβ/49

= 7/2 * 1/49

= 7/98

Therefore, the value of αβ-1 βα-1 is 7/98.

Explanation:

To solve the problem, we first need to find the roots of the given quadratic equation. Once we have the roots, we can apply the formula to find the required value.

We know that the product of the roots of a quadratic equation ax2 + bx + c = 0 is given by c/a, where a, b and c are the coefficients of the equation. In this case, the product of the roots α and β is 7/2.

We also know that the reciprocal of a root is the other root divided by the constant term. Using this, we can find the reciprocals of α and β.

Once we have the values of α, β, α-1 and β-1, we can substitute them in the formula to find the required value.

The final answer is 7/98.