Question

Find the value of 'a' and 'b' :-

5+2√3 / 7+4√3 = a - b√6

Answer 1

Step-by-step explanation:

5+2√3/7+4√3=

5+2√3/7+4√3*7-4√3/7-4√3

we get (5+2√3)(7-4√3)/(7+4√3)(7-4√3)

now multiply numerator and denominator

35-20√3+14√3-24/49-48

11-6√3/1

11-2*3√3

11-3√2√6

a=11 and b=3√2

Answer 2

Answer:

Hey mate ✨

Here's ur answer :

L.H.S = (5 + 2√3)/(7 + 4√3)

Rationalize the denominator,

= (5 + 2√3)(7 + 4√3)/(7 + 4√3)(7 - 4√3)

= [5 × 7 - 5 × 4√3 + 2√3 × 7 - 2√3 × 4√3]/[(7)^2 - (4√3)^2]

Using formula :

(x + y)(x - y) = x^2 - y^2

= [35 - 20√3 + 14√3 - 24]/[49 - 48]

= (11 - 6√3)

Multiplying by √2

= (11√2 - 6√6)

therefore,

L.H.S = R.H.S

11√2 - 6√6 = a - b√6

Comparing both sides

a = 11√2

b = 6

⭕ Hope it helps ⭕