Question

Find the value of
a' and 'b' if
the
equation is
5-√6/
5+√6 is equal to
a-b √6​

Answer 1

Step-by-step explanation:

Given :-

(5-√6)/(5+√6) = a-b √6

To find:-

Find the values of 'a' and 'b'

Solution:-

Given equation is

(5-√6)/(5+√6) = a-b √6

Denominator = 5+√6

We know that

Rationalising factor of a+√b is a-√b

Rationalising factor of 5+√6 = 5-√6

Now On Rationalising the denominator then

=>(5-√6)(5-√6)/(5+√6)+5-√6) = a-b√6

=>(5-√6)^2 / [(5^2-{√6}^2] = a-b√6

Since (a+b)(a-b) = a^2 - b^2

=>[5^2-2(5)(√6)+(√6)^2]/(25-6) = a-b√6

Since (a-b)^2 = a^2-2ab+b^2

=>(25-10√6+6)/(19) = a-b√6

=>(31-10√6)/19 = a-b√6

=>(31/19) - (10/19)√6 = a - b√6

On comparing both sides then

a = 31/19

b= 10/19

Answer:-

The value of a = 31/19

The value of b = 10/19

Used formulae:-

• Rationalising factor of a+√b is a-√b
• (a-b)^2 = a^2-2ab+b^2
• (a+b)(a-b) = a^2 - b^2