Question

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

Answer 1

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}`