Question

(a=root5 +1 /root5-1 ) (b=root 5 -1 /root 5+1 ) find = a^2 + a*b + b^2 /a^2- a*b + b^2

Answer 1

Answer:

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Answer 2

The value of (a²+ab+b²)/(a²-ab+b²) is 4/3.

Given,

The value of a = (√5+1)/(√5-1) and b = (√5-1)/(√5+1).

To Find,

The value of (a²+ab+b²)/(a²-ab+b²).

Solution,

Now, we will find the value of

a+b =  (√5+1)/(√5-1) + (√5-1)/(√5+1)

a+b  3

Now,

a*b = (√5+1)/(√5-1)*(√5-1)/(√5+1)

a*b= 1

Now,

(a²+ab+b²)/(a²-ab+b²) = ((a+b)²-2ab+ab))/((a+b)²-2ab-ab)

(a²+ab+b²)/(a²-ab+b²) = (3²-2+1)/(3²-2-1)
(a²+ab+b²)/(a²-ab+b²) = (9-1)/(9-3)

(a²+ab+b²)/(a²-ab+b²) = 8/6 = 4/3

Hence, the value of (a²+ab+b²)/(a²-ab+b²) is 4/3.

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