Question

find a and b if 3√2+2√3/5√2-4√3=a-b√6

Answer 1

Hiiii friend,

3✓2+2✓3/5✓2-4✓3

Rationalizing the denominator 5✓2-4✓3

=> 3✓2 + 2✓3/5✓2 -4✓3 × 5✓2+4✓3/5✓2+4✓3

=> (3✓2+2✓3)(5✓2+4✓3)/(5✓2-4✓3)(5✓2+4✓3)

=> 3✓2(5✓2+4✓3)+2✓3(5✓2+4✓3)/(5✓2)² - (4✓3)²

=> 30 + 12✓6 + 10✓6 + 24/50 - 48

=> 54+22✓6/2

=> 2(27+11✓6)/3


=> 27+11✓6

Now,

LHS = RHS

27+11✓6 = A+B✓6

Clearly,

A = 27 And B = 11

HOPE IT WILL HELP YOU..... :-)