y is inversely proportional to the square of x - Edexcel - GCSE Maths - Question 17 - 2019 - Paper 3

Using the information that y = 8 when x = 2.5:

Substituting these values into our equation:

$8 = \frac{k}{(2.5)^2}$

This simplifies to:

$8 = \frac{k}{6.25}$

Thus, we can solve for k:

$k = 8 \times 6.25 = 50$

Now substituting y = \frac{8}{9}$ into the established relationship:

$\frac{8}{9} = \frac{50}{x^2}$

Cross-multiplying gives:

$8x^2 = 450$

Dividing both sides by 8:

$x^2 = \frac{450}{8} = 56.25$

Taking the square root:

$x = \pm \sqrt{56.25} = \pm 7.5$

Since we are looking for the negative value, the answer is:

$x = -7.5$