find the values of a and b, if a and b are rational numbers: 5+2√3 / 7+4√3 = a-b√3
Answers
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Step-by-step explanation:
5+2
3
=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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