15 The two values of \(\theta\) that satisfy the equation
$$\sinh ^ { 2 } \theta - \sinh \theta - 2 = 0$$
are \(\theta _ { 1 }\) and \(\theta _ { 2 }\)
15
- Hamzah is asked to find the value of \(\theta _ { 1 } + \theta _ { 2 }\)
He writes his answer as follows:
The quadratic coefficients are \(a = 1 , b = - 1 , c = - 2\)
The sum of the roots is \(- \frac { b } { a }\)
So \(\theta _ { 1 } + \theta _ { 2 } = - \frac { - 1 } { 1 } = 1\)
Explain Hamzah's error.
[0pt]
[1 mark]
15 - Find the correct value of \(\theta _ { 1 } + \theta _ { 2 }\)
Give your answer as a single logarithm.
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