plz help me class 9 math
Answers
Solution :-
(i) √3 - 1/√3 + 1 = a - b√3
The Rationalisation factor for √3 + 1 is √3 - 1 . Therefore , multiplying and dividing by √3 - 1 we have :
= (√3 - 1)(√3 - 1) /(√3 + 1)(√3 - 1)
= (√3 - 1)²/√3² - 1²
By Using Identity : (a - b)² = a² + b² - 2ab & (a + b)(a – b) = a² - b²
= [√3² + 1² - 2 ×√3 × 1 ]/ (3 - 1)
= [3 + 1 - 2√3]/2
= [4 - 2√3]/2
= 2 - √3
We have , √3 - 1/√3 + 1 = a - b√3
2 - √3 = a - b√3
On equating rational and Irrational parts we obtain :
a = 2 , b = 1
Hence rational numbers a is 2 and b is 1.
(ii) 3 + √2 / 3 -√2 = a + b √2
The Rationalisation factor for 3 - √2 is 3 + √2 . Therefore , multiplying and dividing by 3 + √2 we have :
= (3 + √2)(3 + √2) / (3 - √2) (3 + √2)
By Using Identity : (a + b)² = a² + b² + 2ab & (a + b)(a – b) = a² - b²
= [(3 + √2)²]/ (3)² - (√2)²
= [3² + √2² - 2 × 3 × √2 ]/ (9 -2)
= [9 + 2 - 6√2]/ 7
= (11 - 6√2]/ 7
= 11/7 - 6√2/ 7
We have , 3 + √2 / 3 -√2 = a + b √2
11/7 - 6√2/ 7 = a + b √2
On equating rational and Irrational parts we obtain :
a = 11/7, b = 6/7
Hence rational numbers a is 11/7 and b is 6/7.