Question

if 5+2 root3/7+root 3 =a-root 3×b, find a and b where a and b are rational number​

Answer 1

5+2√3/7+√3 = a-√3×b

Lhs=

5+2√3/7+√3×7-√3/7-√3

5+2√3(7-√3)/(7)² - (√3)²

5(7-√3)+2√3(7-√3)/49 - 3

35 - 5√3 + 14√3 - 2×3 / 46

35-5√3+14√3-6/46

35-6-5√3+14√3/46

29+9√3/46

hence, when compared

a=29/46

b=9/46

Answer 2

Answer:29/46;-9/46

Step-by-step explanation:

5+2root3/7+root3

=(5+2root3)(7-root3)/49-3

=35-6+14root3-5root3/46

=29+9root3/46=a-broot3

So 29+9root3=46a-46broot3

46a=29 a=29/46

-46broot3=9root3 so b=-9/46