If a=√5+1/√5-1 and b=√5-1/√5+1, find the value of a^2+ab+b^2/a^2-ab+b^2
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X=√√{(5+1)/(√5−1)(5+1)/(√5−1)}
=√{(√5+1)(√5+1)/(√5+1)(√5–1)} (multiply by (√5+1)
=√{(√5+1)^2/4}
=(√5+1)/2.
Now,5x^2–5x+1
=5x*(x-1)+1
=5* {(√5+1)/2}*{(√5+1)/2–1}+1
=5* {(√5+1)/2}*{(√5–1)/2}+1
=5*4/4 +1
=5+1=6
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