Powers and Roots Practice Test 1

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Question : 3 of 40

Marks: +1, -0

If

{5+2√3}/{7+4√3}=a+b√3

then:

a = 6, b = 11
a = 11, b = –6
a = –11, b = 6
a = –11, b = –6

Solution:

{5+2√3}/{7+4√3}=a+b√3

L.H.S.

={5+2√3}/{7+4√3}×{7-4√3}/{7-4√3}

={35+14√3-20√3-24}/{49-48}

=11-6√3

Now,

a +b√3 =11- 6 √3

Hence, a = 11, b = – 6

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