Solve $(x - 2)^2 = 3$ Give your solutions correct to 3 significant figures. - Edexcel - GCSE Maths - Question 16 - 2017 - Paper 2

To solve the equation, we first take the square root of both sides:

$x - 2 = ext{±} \sqrt{3}$

This gives us two equations:

1. (x - 2 = \sqrt{3})
2. (x - 2 = -\sqrt{3})

Now we can solve for (x) in each case:

1. For the first equation:

   $x = 2 + \sqrt{3}$

   Using a calculator, (\sqrt{3} \approx 1.732), so:

   $x \approx 2 + 1.732 = 3.732$

   Rounding to 3 significant figures gives (x \approx 3.73).

2. For the second equation:

   $x = 2 - \sqrt{3}$

   This leads to:

   $x \approx 2 - 1.732 = 0.268$

   Rounding to 3 significant figures gives (x \approx 0.268).

Thus, the solutions are:

• (x \approx 3.73)
• (x \approx 0.268)