Determine the value of x if the total distance between house a and b by road is 14 km. Distance from house a to church is 2x minus 1, church to garage is x squared plus 2, garage to house b is x squared minus 3

Answer 1

The total distance between house a and b can be expressed as the sum of the distances between each pair of locations:

Distance from house a to church + Distance from church to garage + Distance from garage to house b = 2x - 1 + x^2 + 2 + x^2 - 3 = 14

Combining like terms, we have:

2x - 1 + x^2 + 2 + x^2 - 3 = 14
2x - 1 + 2x^2 - 1 = 14
2x^2 + 2x - 2 = 14
2x^2 + 2x - 16 = 0

Now, we can solve for x by factoring or using the quadratic formula:

2x^2 + 2x - 16 = 0
2(x^2 + x - 8) = 0
2(x + 4)(x - 2) = 0

Therefore, x = -4 or x = 2.

Since x represents a distance, the value of x must be non-negative. Therefore, x must be 2.