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A student thinks of a number - OCR - GCSE Maths - Question 9 - 2021 - Paper 1

Question 9

A student thinks of a number. They square it and then add 6. Their answer is 295. What number is the student thinking of?

Worked Solution & Example Answer:A student thinks of a number - OCR - GCSE Maths - Question 9 - 2021 - Paper 1

Step 1

Set up the equation based on the problem statement

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Answer

Let the number the student is thinking of be represented by the variable $x$ . According to the problem, when this number is squared and then increased by 6, the result is 295. This can be formulated as:

$x^2 + 6 = 295$

Step 2

Solve the equation for x

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Answer

To isolate $x^2$ , subtract 6 from both sides:

$x^2 = 295 - 6$

This simplifies to:

$x^2 = 289$

Step 3

Find the square root of both sides

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Answer

To find the value of $x$ , take the square root of both sides:

$x = rac{\pm ext{sqrt}(289)}{1}$

Thus, we find:

$x = 17 ext{ or } x = -17$

Step 4

Identify the number the student was thinking of

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Answer

Since the problem context suggests a positive number, the final answer is:

$x = 17$

Therefore, the number the student is thinking of is 17.

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