Final answer:
The value of e² + 1/e² given that e - 1/e = 11 is 123 after squaring the given equation and simplifying.
Step-by-step explanation:
To find the value of e² + 1/e² given that e - 1/e = 11, we will start by squaring the given equation to find e² + 1/e² + 2(e)(1/e). Squaring e - 1/e we get e² - 2(e)(1/e) + 1/e² = 121. Since (e)(1/e) = 1, the equation simplifies to e² + 1/e² - 2 = 121. We can then add 2 to both sides to isolate e² + 1/e², giving us e² + 1/e² = 123.