Currently unavailable: for regular students

Degree: Mathematics (Bachelors) - Cambridge University

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Mathematics is a beautiful subject and I always teach Mathematics as such. Mathematics we are introduced to in textbooks can come off as really dry and pointless - it is not so!

When I teach Mathematics, I wish to change the general perception of Mathematics.  I wish for the student to appreciate and love the subject as much as I do. I teach the subject in a fun, light hearted manner explaining the intuition behind the idea rather than showing a method which sometimes works but you have no idea why. Intuition is key to excelling in Mathematics.

#### Subjects offered

SubjectQualificationPrices
Maths A Level £22 /hr
Maths GCSE £20 /hr
Maths IB £22 /hr
Maths 13 Plus £20 /hr
Maths 11 Plus £20 /hr
.MAT. Uni Admissions Test £25 /hr
.STEP. Uni Admissions Test £25 /hr

#### Qualifications

MathematicsA-levelA2A* (99.7%)
Further Mathematics A-levelA2A* (99.7%)
PhysicsA-levelA2A* (99.7%)
 CRB/DBS Standard No CRB/DBS Enhanced No

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### Find all positive integers n such that 12n-119 and 75n-539 are both perfect squares. Let N be the sum of all possible values of n. Find N.

Let 75n - 539 = l^2 and 12n - 119 = k^2 . where n is a natural number. Multiply 75n - 539 = l^2 by 4 to give 300n - 2156 =4l^2 and 12n - 119 = k^2 by 25 to give 300n - 2975 = 25k^2. Subtract the two new expressions to give 4l^2 - 25k^2 = 819 which can be factorised (using the difference of two...Let 75n - 539 = l^2 and 12n - 119 = k^2 . where n is a natural number. Multiply 75n - 539 = l^2 by 4 to give 300n - 2156 =4l^2 and 12n - 119 = k^2 by 25 to give 300n - 2975 = 25k^2. Subtract the two new expressions to give 4l^2 - 25k^2 = 819 which can be factorised (using the difference of two squares) to give (2l - 5k)(2l + 5k) = 819. The prime factorisation of 819 is 3^2 * 7 * 13 There are five cases to consider. Dealing with the cases (noting that 2l - 5k < 2l +5k ) yields that n can only be 20 or 12. Hence N = 20 + 12 = 32. see more

1 year ago

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