Question

郁欣

求解，謝謝🙏

#*#*£ ( √√√√₂+1)* + (√√√²-1)² = 6 x =
gol
±4.
O
ti

Answer 1

✨ 最佳解答 ✨

qn

√2-1 = 1/(√2+1) (即兩根號內的數互為倒數)

設a=√(√2+1), a⁻¹=√(√2-1)
aˣ+a⁻ˣ=6
(aˣ)²-6(aˣ)+1=0
aˣ=(6±√32)/2
=3±2√2

3+2√2=(√2+1)²；3-2√2=(√2+1)⁻²
x=4或-4