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Please help on this practice paper my parents couldn’t solve this either

Please help on this practice paper my parents couldn’t solve this either-example-1

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We are given that ,


{:\implies \quad \sf (12+√(128))/(1-√(2))=a+b√(2)}

Consider LHS;


{:\implies \quad \sf (12+√(128))/(1-√(2))}

Can be further written as ;


{:\implies \quad \sf (12+8√(2))/(1-√(2))}

Rationalizing the denominator we have ;


{:\implies \quad \sf (12+8√(2))/(1-√(2))* (1+√(2))/(1+√(2))}


{:\implies \quad \sf ((12+8√(2))(1+√(2)))/((1-√(2))(1+√(2)))}


{:\implies \quad \sf (12(1+√(2))+8√(2)(1+√(2)))/(1-2)}


{:\implies \quad \sf (12+12√(2)+8√(2)+16)/(-1)}


{:\implies \quad \sf (28+20√(2))/(-1)}


{:\implies \quad \sf -28-20√(2)}

Hence, we can conclude that ;


  • {\bf a=-28}

  • {\bf b=-20}

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