Question

If 5+ 2 root 3 upon
7+root 3 = a-b root3 find the a and b where are a and b are rational numbers
​

Answer 1

Answer:

Step-by-step explanation:

Given :

To find : Value of a and b

Solution :

Consider Left Hand Side

Rationalize the denominator

The Rationalizing factor of 7 + √3 is 7 - √3 . So, Multiply numerator and denominator with rationalising factor.

Since (x + y)(x - y) = x² - y²

Now Consider,

Equating to the corresponding rational and irrational number we have ,

Identity used :-

(x + y)(x - y) = x² - y²

Extra info related to the question :-

What is a rationlising factor ?

If the product of two irrational numbers is a rational number then each of the the two is rationalising factor of the other.

How to rationalise the denominator ?

1) Consider the denominator of the fraction.

2) Then multiply the numerator and denominator with rationalising factor of the denominator.

Answer 2

Answer:

5 + 2√3 / 7 + √3 = a - b√3

LHS :-

= 5 + 2√3 / 7 + √3

= Multiply both sides by √3 .

= 5 + 2√3 * 7 - √3 / 7 + √3 * 7 - √3

= 35 - 5√3 + 14√3 - 6 / 49  - 3

= 29 + 9√3 / 46

so , a = 29 / 46

    b = 9 / 46

Step-by-step explanation:

Please follow and mark me as brainliest .