Question

If 'a' and 'b' are two rational numbers such that 3+2√3 / 3-2√3=a+b√3, find the values of 'a' and 'b' respectively.
CLASS 9 CBSE
CHAPTER-NUMBER SYSTEMS
PLZ HELP​

Answer 1

Answer:

Step-by-step explanation:

3 + 2√3 / 3 - 2√3 = a + b√3

L.H.S

3 + 2√3 / 3 - 2√3

//multiply numerator and denominator by 3 + 2√3

=> 3 + 2√3 / 3 - 2√3   *  3 + 2√3 / 3 + 2√3

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

//Denominator is of form (a + b)(a-b) which is equal to a² - b²

=> (3 + 2√3)² / (3)² - (2√3)²

=> (3 + 2√3)² / 9 - 12

=> (3 + 2√3)²/-3

//we know that (a+b)² = a² + b² + 2ab

=> -1/3[(3)² + (2√3)² + 2(3)(2√3)]

=> -1/3[9 + 12 + 12√3]

=> -21/3 - 12√3/3

=> -7 - 4√3

Given it is equal to a + b√3

=> (-7) + (-4)√3 = a + b√3

Thus a = -7, b = -4.