Answer:
1154
Step-by-step explanation:
Perhaps the easiest way to evaluate this numerical expression is to let a calculator do it. Alternatively, we can compute the value from a +1/a.
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expression
Consider the square of a +1/a:
(a +1/a)^2 = a^2 +2(a)(1/a) +1/a^2 = (a^2 +1/a^2) +2
This means ...
a^2 +1/a^2 = (a +1/a)^2 -2
Similarly, using a^2 for 'a' in the above, we have ...
a^4 +1/a^4 = (a^2 +1/a^2)^2 -2
numerical value
The value of a +1/a is ...
[tex]a+\dfrac{1}{a}=3-2\sqrt{2}+\dfrac{1}{3-2\sqrt{2}}=(3-2\sqrt{2})+\dfrac{3+2\sqrt{2}}{3^2-(2\sqrt{2})^2}\\\\=(3-2\sqrt{2})+(3+2\sqrt{2})\\\\a+\dfrac{1}{a}=6[/tex]
Then the value of a^2 +1/a^2 is 6^2 -2 = 34
and the value of a^4 +1/a^4 is 34^2 -2 = 1154
