Photo AI

Write down the x-coordinates of the points where y = x^2 - x and y = x + 1 cross. - OCR - GCSE Maths - Question 22 - 2020 - Paper 3

Question 22

Write down the x-coordinates of the points where y = x^2 - x and y = x + 1 cross.

Worked Solution & Example Answer:Write down the x-coordinates of the points where y = x^2 - x and y = x + 1 cross. - OCR - GCSE Maths - Question 22 - 2020 - Paper 3

Step 1

96%

114 rated

Answer

To find the x-coordinates at which the two curves intersect, set the equations equal to each other:

$x^2 - x = x + 1$

Step 2

99%

104 rated

Answer

Rearranging gives:

$x^2 - 2x - 1 = 0$

Step 3

96%

101 rated

Answer

Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where (a = 1), (b = -2), and (c = -1):

$x = \frac{2 \pm \sqrt{(-2)^2 - 4 \cdot 1 \cdot (-1)}}{2 \cdot 1}$

This simplifies to:

$x = \frac{2 \pm \sqrt{4 + 4}}{2} = \frac{2 \pm \sqrt{8}}{2} = 1 \pm \sqrt{2}$

Step 4

98%

120 rated

Answer

Thus, the x-coordinates where the curves cross are:

$x = 1 + \sqrt{2}$ and $x = 1 - \sqrt{2}$

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;