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Identity (x+y)(x-y)

If a =√3+1 / ...

Question

If a=√3+1/√3-1 and b=1/a,find the value of a^2-b^2+ab

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Solution

a=√3+1/√3-1
=(√3+1/√3-1)(√3+1/√3+1)
On solving
a=(4+2√3)/2=2+√3
a²=(2+√3)²=7+4√3

b²=1/a²=1/(7+4√3)=7-4√3

ab=a(1/a)=1

a²-b²+ab= (7+4√3)-(7-4√3)+1 = 1+8√3

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