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Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 26 - 2023 - Paper 1

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Here is a table of values for $y = \frac{6}{x} - 2x$. | x | -4 | -3 | -2 | -1 | 2 | 3 | 4 | |-------|------|------|------|------|------|------|... show full transcript

Worked Solution & Example Answer:Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 26 - 2023 - Paper 1

Step 1

Draw the graph of $y = \frac{6}{x} - 2x$ for $-4 < x < 4, x \neq 0$

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Answer

To draw the graph, plot the points given in the table:

  • At x=−4x = -4, y=6.5y = 6.5
  • At x=−3x = -3, y=4y = 4
  • At x=−2x = -2, y=1y = 1
  • At x=−1x = -1, y=−1y = -1
  • At x=2x = 2, y=1y = 1
  • At x=3x = 3, y=4y = 4
  • At x=4x = 4, y=6.5y = 6.5

Connect these points smoothly to depict the behavior of the function, ensuring that the graph does not exist at x=0x = 0.

Step 2

Use your graph to find the positive solution of $\frac{6}{x} - 2x = 0$

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Answer

To solve 6x−2x=0\frac{6}{x} - 2x = 0, we can rearrange it as follows:

  1. Start by multiplying through by xx (noting that x≠0x \neq 0): 6−2x2=06 - 2x^2 = 0
  2. Rearranging gives us: 2x2=62x^2 = 6
  3. Dividing both sides by 2 yields: x2=3x^2 = 3
  4. Taking the square root gives us: x=3≈1.732x = \sqrt{3} \approx 1.732

Using the graph, we can find this value around x=1.7x = 1.7. Hence, the answer rounded to 1 decimal place is:

x=1.7x = 1.7.

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