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

Question 16

Solve $(x - 2)^2 = 3$ Give your solutions correct to 3 significant figures.

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

Step 1

Step 1: Rearranging the Equation

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Answer

To solve for $x$ , we start by isolating the squared term. We rewrite the equation as: $(x - 2)^2 = 3$

Step 2

Step 2: Taking the Square Root

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Answer

Next, we take the square root of both sides, keeping in mind that we will have both a positive and a negative solution: $x - 2 = rac{ ext{\pm} ext{sqrt}(3)}{1}$

Step 3

Step 3: Solving for x

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Answer

Now, we add 2 to both sides to isolate $x$ : $x = 2 ext{ ± } ext{sqrt}(3)$

Calculating the numerical values:

For the positive root: $x ext{ (positive)} = 2 + ext{sqrt}(3) \ ext{ which is approximately } 3.732$
For the negative root: $x ext{ (negative)} = 2 - ext{sqrt}(3) \ ext{ which is approximately } 0.268$

Step 4

Step 4: Final Solutions

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Answer

Thus, the final solutions correct to 3 significant figures are:

$x ext{ (positive)} = 3.73$
$x ext{ (negative)} = 0.268$

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