Find the real root of the equation $$$\frac{2 \mathrm{e}^{x}+\mathrm{e}^{-x}}{2+\mathrm{e}^{x}}=3$$$, giving your answer correct to 3 decimal places. Your working should show clearly that the equation has only one real root. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_31 Year：2021 Question No：2

Answer:

Reduce to a 3-term quadratic $ u^{2}+6 u-1=0 $ OE
Solve a 3-term quadratic for $u$
Obtain root $\sqrt{10}-3$
Obtain answer $x=-1.818$ only
Reject $-\sqrt{10}-3$ correctly
Alternative method for Question 2
Rearrange to obtain a correct iterative formula
Use the iterative process at least twice
Obtain answer $x=-1.818$
Show sufficient iterations to at least 4 d.p. to justify $x=-1.818$
Clear explanation of why there is only one real root

Knowledge points:

3.2.3 use logarithms to solve equations and inequalities in which the unknown appears in indices

Answer:

Knowledge points:

Solution:

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