1.7 Lösning 9
Från Mathonline
\[ \, (P + Q) \, = \, 2\,^x \, + \, 2\,^{-x} \; + \; 2\,^x \, - \, 2\,^{-x} \, = \, 2\,^x \, + \, 2\,^x \; + \; 2\,^{-x} \, - \, 2\,^{-x} \, = \, 2 \cdot 2\,^x \]
\[ \, (P - Q) \, = \, 2\,^x \, + \, 2\,^{-x} \; - \; (2\,^x \, - \, 2\,^{-x}) \, = \, 2\,^x \, + \, 2\,^{-x} \; - \; 2\,^x \, + \, 2\,^{-x} \, = \, \]
- \[ \, = \, 2\,^x \, - \, 2\,^x \; + \; 2\,^{-x} \, + \, 2\,^{-x} \, = \, 2 \cdot 2\,^{-x} \]
\[ \, (P + Q) \cdot (P - Q) \, = \, 2 \cdot 2\,^x \, \cdot \, 2 \cdot 2\,^{-x} \, = \, 2 \cdot 2 \, \cdot \, 2\,^x \cdot 2\,^{-x} \, = \, 4 \, \cdot \, 2\,^{x\,-\,x} \, = \, \]
- \[ \; = \, 4 \, \cdot \, 2\,^0 \, = \, 4 \]
