Maths-
General
Easy

Question

if fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction plus fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction equals a plus b square root of 5. Then, find the values of a and b.

The correct answer is: Values are a and b 42/11 and 0




    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 text  Let's say  end text x equals fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction text  and  end text y equals fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction end cell row cell text  so,  end text x plus y equals a plus b square root of 5 end cell end table

    fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction plus fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction 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 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction cross times fraction numerator 4 plus square root of 5 over denominator 4 plus square root of 5 end fraction equals fraction numerator left parenthesis 4 plus square root of 5 right parenthesis squared over denominator 16 minus 5 end fraction equals fraction numerator 16 plus 5 plus 2 cross times 4 cross times square root of 5 over denominator 11 end fraction equals fraction numerator 21 plus 8 square root of 5 over denominator 11 end fraction end cell row cell y equals fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction cross times fraction numerator 4 minus square root of 5 over denominator 4 minus square root of 5 end fraction equals fraction numerator left parenthesis 4 minus square root of 5 right parenthesis squared over denominator 16 minus 5 end fraction equals fraction numerator 16 plus 5 minus 2 cross times 4 cross times square root of 5 over denominator 11 end fraction equals fraction numerator 21 minus 8 square root of 5 over denominator 11 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 21 plus 8 square root of 5 over denominator 11 end fraction plus fraction numerator 21 minus 8 square root of 5 over denominator 11 end fraction equals a plus b square root of 5 end cell row cell fraction numerator 21 plus 8 square root of 5 plus 21 minus 8 square root of 5 over denominator 11 end fraction equals a plus b square root of 5 end cell row cell 42 over 11 equals a plus b square root of 5 end cell end table
    So by comparing we found that, straight a equals 42 over 11 text  and  end text straight b equals 0
    Final Answer:
    Hence, the value of a is 42 over 11 and b is 0.

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