If a = 2-√5/2+√5 & b = 2+√5/2-√5 then find the value of (a+b)³
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a=2-√5/2+√5
b=2+√5/2-√5
Now a+b=2-√5/2+√5 +2+√5/2-√5
={(2-√5)^2+(2+√5)^2}/(2-√5)(2+√5)
=2{(2)^2+(√5)^2}/{(2)^2-(√5)^2}
=2{4+5)/(4-5)
=2×9/-1
= -18
ab=2-√5/2+√5 ×2+√5/2-√5=1
therefore (a+b)^3
=(a+b)^3-3ab(a+b)
=(-18)^3-3×1×(-18)
=5832+54
=5886
b=2+√5/2-√5
Now a+b=2-√5/2+√5 +2+√5/2-√5
={(2-√5)^2+(2+√5)^2}/(2-√5)(2+√5)
=2{(2)^2+(√5)^2}/{(2)^2-(√5)^2}
=2{4+5)/(4-5)
=2×9/-1
= -18
ab=2-√5/2+√5 ×2+√5/2-√5=1
therefore (a+b)^3
=(a+b)^3-3ab(a+b)
=(-18)^3-3×1×(-18)
=5832+54
=5886
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