Question

If a =√3+1/√3-1and b=1/a find the value of a²+ab+b².
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Answer 1

Step-by-step explanation:

If a = 1 + √3 and b = 1 - √3, what is the value of (a2 + b2)? ... a² = (1 + √3)² = (1 + √3)(1 + √3) = 1 + 2√3 + √9 = 1 + 2√3 + 3 b² ... If a - b = 3 and a2 + b2 = 29, 

Answer 2

a =√3+1/√3-1
Rationalise the denominator

a =√3+1/√3-1 x √3+1/√3+1
a= (√3+1)^2/3-1
a=3+1+2√3 / 2= 4+2√3 / 2
a= =2+√3

b=1/a = 1/2+√3
Rationalise the denominator

b=1/a = 1/2+√3 x 2-√3/2-√3
b= 2-√3/4-3
b= 2-√3


a²+ab+b²=(a+b)^2
=(2+√3 +2-√3)^2 = 4^2=16

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