Question

If $$(x - 2)$$, $$(x + 2)$$, $$(2x + 1)$$ and $$(2x + 19)$$ are in proportion, find the value of $$x$$.

Answer 1

Since the given terms are in proportion:

$$(x - 2)(2x + 19) = (x + 2)(2x + 1)$$

Expanding both sides:

$$2x^2 + 19x - 4x - 38 = 2x^2 + x + 4x + 2$$

$$2x^2 + 15x - 38 = 2x^2 + 5x + 2$$

Simplifying: $$15x - 5x = 2 + 38$$

$$10x = 40$$

$$x = 4$$

Hence, the value of $$x$$ is 4.