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1.

x = (5√2 + 2√5) / (5√2 - 2√5)，
y = (5√2 - 2√5) / (5√2 + 2√5) = 1/x

(1)

x=(5√2 + 2√5) / (5√2 - 2√5)
=(5√2 + 2√5)²/30
=(70+20√10)/30

y=(5√2 - 2√5) / (5√2 + 2√5)
=(5√2 - 2√5)²/30
=(70-20√10)/30

∴x+y=(70+20√10)/30+(70-20√10)/30
=(70+20√10+70-20√10)/30
=140/30
=14/3

(2)

x²+y²
=(x+y)²-2xy
=(14/3)²-2*x*(1/x)
=196/9-2
=178/9

2.

√49 - √0.36 + √(-5)² - √81/4 + √1+9/16

=√49 - √0.36 + √25 - √81/4 + √25/16

=7-0.6+5-9/2+5/4

=8.15

3.

1 - 2√3 + √5 / (1-√3) (√5-√3)

=1 - 2√3 + √5(1-√3) / (1²-√3²)(√5-√3)

=1 - 2√3 + √5(1-√3) / (-2)(√5-√3)

=1 - 2√3 + √5(1-√3)(√5+√3) / (-2)(√5²-√3²)

=1 - 2√3 + √5(1-√3)(√5+√3) / (-2)(2)

=1 - 2√3 + √5(-3+√5+√3-√15) / (-4)

=1 - 2√3 + (-3√5+5+√15-5√3) / (-4)

=(5-5√3-3√5+√15-4+8√3)/ (-4)

=(1+3√3-3√5+√15)/(-4)

第三題的答案很醜,不知道題目有沒有給錯,請提問者再行確認.

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