Question

Find a,b if 5 +√3 / √37 - 4√39 = 47a - b

Answer 1

Step-by-step explanation:

5+√3/(7-4√3)

→ 5+√3/7-4√3 × 7+4√3/7+4√3

→ (5+√3)(7+4√3)/(7-4√3)(7+4√3)

→ 5(7+4√3)+√3(7+4√3)/{7²-(4√3)²}

→ 35+20√3+7√3+4(3)/(49-16(3))

→ 35+20√3+7√3+12/(49-48)

→ 47+27√3/1

→ 47+27√3 = 47a+√3b

Therefore,by comparing we can say that

a = 1 and b = 27