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Question

If fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction plus fraction numerator square root of 5 minus 1 over denominator square root of 5 plus 1 end fraction equals a plus b square root of 5   Find the values of a and b

hintHint:

Hint:
Rationalization is a technique which is used to eliminate the irrational number in the denominator. For example,fraction numerator 1 over denominator square root of 3 end fraction
can be rationalised as fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction

The correct answer is: Values are a and b is 3 and 0


    fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction plus fraction numerator square root of 5 minus 1 over denominator square root of 5 plus 1 end fraction equals a plus b square root of 5
    Let’s say  x equals fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction text  and  end text y equals fraction numerator square root of 5 minus 1 over denominator square root of 5 plus 1 end fraction
    so,x plus y equals a plus b square root of 5
    Step 1 of 2:
    Rationlising both x and y
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction cross times fraction numerator square root of 5 plus 1 over denominator square root of 5 plus 1 end fraction equals fraction numerator left parenthesis square root of 5 plus 1 right parenthesis squared over denominator 5 minus 1 end fraction equals fraction numerator 5 plus 1 plus 2 cross times square root of 5 cross times 1 over denominator 4 end fraction equals fraction numerator 6 plus 2 square root of 5 over denominator 4 end fraction end cell row cell y equals fraction numerator square root of 5 minus 1 over denominator square root of 5 plus 1 end fraction cross times fraction numerator square root of 5 minus 1 over denominator square root of 5 minus 1 end fraction equals fraction numerator left parenthesis square root of 5 minus 1 right parenthesis squared over denominator 5 minus 1 end fraction equals fraction numerator 5 plus 1 minus 2 cross times square root of 5 cross times 1 over denominator 4 end fraction equals fraction numerator 6 minus 2 square root of 5 over denominator 4 end fraction end cell end table
    Step 2 of 2:
    Put the values of x and y in equation (1)
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 6 plus 2 square root of 5 over denominator 4 end fraction plus fraction numerator 6 minus 2 square root of 5 over denominator 4 end fraction equals a plus b square root of 5 end cell row cell fraction numerator 6 plus 2 square root of 5 plus 6 minus 2 square root of 5 over denominator 4 end fraction equals a plus b square root of 5 end cell row cell 12 over 4 equals a plus b square root of 5 end cell row cell 3 equals a plus b square root of 5 end cell end table
    So by comparing we found that, a =  and b = 0
    Final Answer:
    Hence, the value of a is  and b is 0.

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