Question

If 1\√12+2√11=a+√b then find a+b
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Answer 1

Given :  1/(√ (12 +  2√11)  = a+√b

To find : a + b

Solution:

1/(√ (12 +  2√11)

= 1/ √ (√11 + 1 +  2√11)

=  1/ √ ((√11 + 1)²)

= 1/ (√11 + 1)

= (√11 - 1)/(11 - 1)

= (√11 - 1)/10

= -1/10  + √11 /10

= -1/10 + √(11 /100)

Comparing with

a + √b

a  = - 1/10

b = 11/100

a  + b  =  -1/10  + 11/100

= 1/100

a  + b  = 1/100

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