simplify 1/7+4 root 3 + 1/2+root5
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Answer:
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Step-by-step explanation:
Solution
verified
Verified
7+4
3
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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Step-by-step explanation:
given :
simplify 1/7+4 root 3 + 1/2+root5
to find :
1/7+4 root 3 + 1/2+root5
solution :
- =1/7+4√3
- x7-4√3/7-4√3==1/2+√5x2-√5/2-√5
- =7-4√3/(7)^2-(4√3)2=2-√5/(2)^2-(√5)^2
- -7-4-√3/49-16×3=2-√5/4-5
- -7-4-√3/49-48-2-√5/-1
- =7-4√3/1-2-√5-1
- 7-4√3+2-√5
- =-5+4√3+√5
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