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If 5+2√3÷7+4√3 = x+y√3 find x & y |
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Answer» Answer: 5+2
=a+b 3
Since RATIONALIZATION of C+ d
a+ b
= c+ d
a+ b
× c− d
c− d
Taking L.H.S. By rationalization, 7+4 3
5+2 3
= 7+4 3
5+2 3
× 7−4 3
7−4 3
Since, {(a+b)(a−b)=a 2 −b 2 } = [(7) 2 −(4 3
) 2 ] (5+2 3
)×(7−4 3
)
= 49−16 3
3
35+14 3
−20 3
−8 3
3
= 49−48 35− 3
(14−8)−24
= 1 35− 3
(6)−24
=11−6 3
Hence, by comparing a = 11 & b = -6. |
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