MYTUTOR SUBJECT ANSWERS

749 views

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 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.
Soham K. A Level Maths tutor, 13 plus  Maths tutor, IB Maths tutor, G...

1 year ago

Answered by Soham, an Uni Admissions Test .STEP. tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

23 SUBJECT SPECIALISTS

£26 /hr

Ana S.

Degree: Physics (Bachelors) - Oxford, Balliol College University

Subjects offered:.STEP., Physics+ 3 more

.STEP.
Physics
Maths
.PAT.
-Oxbridge Preparation-

“A friendly and understanding tutor with three years experience in school clubs, summer camps and private tutoring.”

£36 /hr

Joe B.

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered:.STEP., Maths+ 3 more

.STEP.
Maths
Further Mathematics
.MAT.
-Personal Statements-

“Hi! I'm Joe, a friendly, experienced and patient tutor with in-depth knowledge of both the old and new A Level Maths & Further Maths specifications.”

PremiumGeorge B. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...
£28 /hr

George B.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:.STEP., Maths+ 1 more

.STEP.
Maths
Further Mathematics

“Fourth year undergraduate at one of the top universities for Maths. Eager to tutor and help improve your grades.”

About the author

Soham K.

Currently unavailable: for regular students

Degree: Mathematics (Bachelors) - Cambridge University

Subjects offered:.STEP., Maths+ 1 more

.STEP.
Maths
.MAT.

“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 ...”

MyTutor guarantee

You may also like...

Other Uni Admissions Test .STEP. questions

Show that if a polynomial with integer coefficients has a rational root, then the rational root must be an integer. Hence, show that x^n-5x+7=0 has no rational roots.

By use of calculus, show that x − ln(1 + x) is positive for all positive x.

Show that substituting y = xv, where v is a function of x, in the differential equation "xy(dy/dx) + y^2 − 2x^2 = 0" (with x is not equal to 0) leads to the differential equation "xv(dv/dx) + 2v^2 − 2 = 0"

How can I integrate e^x sin(x)?

View Uni Admissions Test .STEP. tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok