Question

find the value of a b if root 5 + root 3 upon root 5 minus root 3 is equal to a + root 15 b

Answer 1

Given: The equation: root 5 + root 3 upon root 5 minus root 3 is equal to a + root 15 b

To find: The value of a and b.

Solution :

• Now we have provided the term root 5 + root 3 upon root 5 minus root 3 is equal to a + root 15 b.

• In mathematical form, it can be written as:

                √5 + √3 / √5 - √3 = a + b√15

• Now lets consider LHS, we have:

                √5 + √3 / √5 - √3

• Rationalising the denominator, we get:

                (√5 + √3 / √5 - √3)  x (√5 + √3 / √5 + √3  )

                (√5 + √3)² / √5² - √3²

                5 + 3 + 2√15 / 5 - 3

                8 + 2√15 / 2

                4 + √15                  

• Now comparing it with RHS, we get:

                4 + √15 = a + b√15

                a = 4, b = 1

Answer:

         So the value of a is 4 and b is 1.