2022 · Q1
x² - 20 = √(20+√(20+√(20+…))), then what is x equal to?
Elementary MathematicsAlgebra
- A4
- B5
- C√5
- D2√5
Explanation
Let t denote the infinite nested radical. Then t² = 20 + t, i.e. t² − t − 20 = 0, giving t = 5 (the positive root). Hence x² − 20 = 5, so x² = 25 and x = 5 (the negative root −5 is not among the options). The keyed option is B.