Question

11. If a and b are rational numbers, find the value of a and b in :
a. (root 3-1)/( root 3+1)= a + b root 3
b. (root 2 +root 3) (3 root 2-2 root 2) = a-b root 6.​

Answer 1

Answer:

(√2 + √3)/( 3√2 -2√3) = a -b√6

( √2 + √3)( 3√2 + 2√3)/{ (3√2)² - (2√3)² }

(6 + 3√6 + 2√6 + 6 )/( 18 - 12)

(12 + 5√6)/6

2 +( 5/12)√6 = a - b√6

so, a = 2 and b = - 5/12

true

Answer 2

Step-by-step explanation:

a) First you have to rationalize the denominator by multiplying both numerator and denominator with root 3-1

then you will get{ root 3 + 1 }2/{root 3}2- {1}2

that will be = 4+2*root3  /2

2{2+root 3 } / 2{1}

and finally you are left with 2+root3

therefore, a = 2 and b =1