Question

If √2-√3/3√2+2√3=a+b√6 where a and b are rational numbers, then find the values of a and b. Plz

Answer 1

(√2 - √3)/(3√2 + 2√3) = a + b√6

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

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

={ 6 -2√6 -3√6+6 }/{ 18 - 12}

={ 12 - 5√6 }/6

=2 - (5/12)√6 = a + b√6

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

Answer 2

Answer:

hey mate! hope it helps u

Step-by-step explanation:

(√2 - √3)/(3√2 + 2√3) = a + b√6

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

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

={ 6 -2√6 -3√6+6 }/{ 18 - 12}

={ 12 - 5√6 }/6

=2 - (5/12)√6 = a + b√6

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