[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

19509 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

By forming and solving a quadratic equation, solve the equation 5*cosec(x) + cosec^2(x) = 2 - cot^2(x) in the interval 0<x<2*pi, giving the values of x in radians to three significant figures.


Differentiate the function X^4 - (20/3)X^3 + 2X^2 + 7. Find the stationary points and classify.


You are given that n is a positive integer. By expressing (x^2n)-1 as a product of factors, prove that (2^2n)-1 is divisible by 3.


Find the equation of the straight line that passes through the points (1,2) and (2,4)


We're here to help

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