Question

find a & b such that
√3+√2÷√3-√2=a+b√b​

Answer 1

(√3+√2) ÷ (√3-√2)

By rationalizing

(√3+√2)² ÷ ( 3 - 2 )

= 3+2+2√3 √2

=5+2√6

Answer 2

Answer:

a = 5 , b = 2

Solution:

Given : (√3 + √2) / (√3 - √2) = a + b√6

To find : a = ? , b = ?

We have ;

a + b√6 = (√3 + √2) / (√3 - √2)

Now,

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

a + b√6

= (√3 + √2)(√3 + √2)/ (√3 - √2)(√3 + √2)

= (√3 + √2)² / [ (√3)² - (√2)² ]

= (3 + 2 + 2•√3•√2) / (3 - 2)

= (5 + 2√6) / 1

= 5 + 2√6

Thus,

a + b√6 = 5 + 2√6

Now,

Comparing the like terms on both sides of above equation , we get ;

a = 5 and b = 2

Hence,

a = 5

b = 2