Question

Find the value of a and b.
3+root 2 / 3- root 2 = a+b root 2

Answer 1

Answer:

3+√2/3-√2

rationalising

3+√2/3-√2 ×3+√2/3+√2

(3+√2)^2/3×3-√2×√2. identity:(a+b) (a-b)=a^2-b^2

9+2+3(√2)(2)/9-2

11+6√2/7

11/7+6√2/7

therefore,a=11/7 b=6/7

Answer 2

Answer:

a=11/7 and b=6/7

Step-by-step explanation:

LHS

Rationalizing the term by multiplying numerator and denominator by 3+$\sqrt{2$ we get

(3+root2)^2/ (3-root2)(3+root2)

using (a-b)(a+b) =a^2-b^2 in denominator and squaring in numerator

=(9 + 2 +6 root2)/9-2

=(11+ 6 root2)/7

comparing with RHS

a=11/7 and b=6/7