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a=√5-√2/√5+√2
=(√5-√2)(√5-√2)/(√5+√2)(√5-√2)
={(√5)²-2.√5.√2+(√2)²}/{(√5)²-(√2)²}
=(5-2√10+2)/(5-2)
=(7-2√10)/3
b=√5+√2/√5-√2
=(√5+√2)(√5+√2)/(√5-√2)(√5+√2)
={(√5)²+2.√5.√2+(√2)²}/{(√5)²-(√2)²}
=(5+2√10+2)/(5-2)
=(7+2√10)/3
Now, a²+ab+b²
=(a+b)²-ab
={(7-2√10)/3+(7+2√10)/3}²-{(7-2√10)/3×(7+2√10)/3}
={(7-2√10+7+2√10)/3}²-(7-2√10)/(7+2√10)
=(14/3)²-{(7-2√10)(7-2√10)/(7+2√10)(7-2√10)}
=196/9-(7-2√10)²/{(7)²-(2√10)²}
=196/9-(49-2.7.2√10+40)/(49-40)
=196/9-(9-28√10)/9
=(196-9+28√10)/9
=(187+28√10)/9
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