[FP2] Solve: 3 cosh x - 4 sinh x = 7

First write cosh and sinh as exponentials, from their respective definitions:sinh x = 1/2 (e - e-x)cosh x = 1/2 (e + e-x​)So: 3 * 1/2 (e + e-x​) - 4 * 1/2 (e - e-x) = 7Multiply by 2: 3 * (e + e-x​) - 4 * (e - e-x) = 14Expanding gives: 3 * e + 3 * e-x  - 4 * e+ 4 * e-x = 14Collecting terms: -ex + 7 * e-x = 14So:  ex - 7 * e-x + 14 = 0Since ex is not 0, we can multiply by it:ex * ex - 7 * e-x *e+ 14 * ex = 0e2x - 7 + 14 * ex = 0This is a quadratic in ex, and we can use the quadratic formula to obtain:ex = -7 +- 2 root 14But ex > 0, so we discount the negative root:ex = -7 + 2 root 14x = ln ( -7 + 2 root 14)Which can easily be checked with a calculator.

Answered by William U. Maths tutor

19937 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find values of x for which 2x^2 < 5x + 12


Differentiate x^x


Express 3(x^2) - 12x + 5 in the form a(x - b)^2 - c.


What is a stationary point and how do I find where they occur and distinguish between them?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences