Question

6-4 under eoot 2/ 6+4 under root 2= a+ b under root 2

Answer 1

Answer:

a = 17

b = -12

Solution:

Given: (6 - 4√2)/(6 + 4√2) = a + b√2

To find: a = ? , b = ?

We have ;

a + b√2 = (6 - 4√2)/(6 + 4√2)

Now,

Rationalising the denominator of the term in RHS , we have ;

a + b√2

= (6 - 4√2)(6 - 4√2)/(6 + 4√2)(6 - 4√2)

= (6 - 4√2)² / {6² - (4√2)²}

= {6² + (4√2)² - 2•6•4√2} / (36 - 32)

= (36 + 32 - 48√2) / 4

= (68 - 48√2) / 4

= 68/4 - 48√2/4

= 17 - 12√2

Thus,

a + b√2 = 17 - 12√2

a + b√2 = 17 + (-12)√2

Now,

Comparing the like terms both the sides ,

We get ; a = 17 and b = -12

Hence,

a = 17

b = -12