Question

Solve the equation 4cosh x+ex=7
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Answer 1

Answer:

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

First write cosh and sinh as exponentials, from their respective definitions:sinh x = 1/2 (ex - e-x)cosh x = 1/2 (ex + e-x)So: 3 * 1/2 (ex + e-x) - 4 * 1/2 (ex - e-x) = 7Multiply by 2: 3 * (ex + e-x) - 4 * (ex - e-x) = 14Expanding gives: 3 * ex + 3 * e-x - 4 * ex + 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 *ex + 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.

Step-by-step explanation:

Hope it helps.

Answer 2

Answer:

$4coshx+e^{x} =7$

Step-by-step explanation:

since $coshx =\frac{1}{2}( \, e^{x}+e^{-x}) \,$

$4coshx+e^{x} =4.\frac{1}{2}( \, e^{x}+e^{-x}) \,+e^{x}$                  

                   $=2 e^{x}+2e^{-x}+e^{x}$                               since $e^{x}=2$ and $e^{-x}= \frac{1}{2}$

                   $=2.2+2.\frac{1}{2} +2$

                   $=4+1+2=7$