Question

If 5 + 2 root 3 / 7 + 4 root 3 = a + b root 3, find a and b.

Answer 1

lhs = (5+2√3)/(7+4√3)

= [(5+2√3)(7-4√3)]/[(7-4√3)(7+4√3)]
=[35-20√3+14√3-24]/[7²-(4√3)²]
=[11-6√3]/[49-48]
=11-6√3
therefore
11-6√3 = a+b√3

compare both sides
a= 11, b= -6

Answer 2

Answer: a = 11 and b = 6.

Step-by-step explanation:

(5 + 2√3)/(7 + 4√3) = a – b√3

By rationalizing the denominator in LHS,

(5 + 2√3)/(7 + 4√3) = a – b√3

[(5 + 2√3)/(7 + 4√3)] × [(7 – 4√3)/(7 – 4√3)] = a – b√3

(5 + 2√3)(7 – 4√3)/ [72 – (4√3)2] = a – b√3

[35 – 20√3 + 14√3 – 24]/(49 – 48) = a – b√3

(11 – 6√3)/1 = a – b√3

11 – 6√3 = a – b√3

Therefore, a = 11 and b = 6.

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