show that: (1/√3-√8)-(1/√8-√7)+(1/√7-√6)-(1/√6-√5)+(1/√5-√2)=5
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Answer:
We have,
(3−
8
)
1
−
(
8
−
7
)
1
+
(
7
−
6
)
1
−
(
6
−
5
)
1
+
(
5
−2)
1
=5
L.H.S.
(3−
8
)
1
−
(
8
−
7
)
1
+
(
7
−
6
)
1
−
(
6
−
5
)
1
+
(
5
−2)
1
By rationalize every part and we get
(3−
8
)
1
×
(3+
8
)
(3+
8
)
−
(
8
−
7
)
1
×
(
8
+
7
)
(
8
+
7
)
+
(
7
−
6
)
1
×
(
7
+
6
)
(
7
+
6
)
−
(
6
−
5
)
1
×
(
6
+
5
)
(
6
+
5
)
+
(
5
−2)
1
×
(
5
+2)
(
5
+2)
=
(9−8)
(3+
8
)
−
8−7
(
8
+
7
)
+
7−6
(
7
+
6
)
−
6−5
(
6
+
5
)
+
5−4
(
5
+2)
=3+
8
−
8
−
7
+
7
+
6
−
6
−
5
+
5
+2
=3+2=5
R.H.S
Hence proved.
Step-by-step explanation:
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