rationalise root 3-1/root3+1
Answers
Answered by
1
Answer:
(a+b)
2
=a
2
+b
2
+2ab
(a+b)(a−b)=a
2
−b
2
Now,
\begin{gathered}\frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } \\\end{gathered}
3
−1
3
+1
On rationalizing the denominator we get,
\begin{gathered}= \frac{ \sqrt{3} + 1 }{ \sqrt{3} - 1} \times \frac{ \sqrt{3} + 1 }{ \sqrt{3} + 1 } \\ \\ = \frac{ {( \sqrt{3}) }^{2} + {(1)}^{2} + 2( \sqrt{3})(1) }{ {( \sqrt{3}) }^{2} - {(1)}^{2} } \\ \\ = \frac{3 + 1 + 2 \sqrt{3} }{3 - 1} \\ \\ = \frac{4 + 2 \sqrt{3} }{2} \\ \\ = \frac{2(2 + \sqrt{3}) }{2} \\ \\ = 2 + \sqrt{3}\end{gathered}
=
3
−1
3
+1
×
3
+1
3
+1
=
(
3
)
2
−(1)
2
(
3
)
2
+(1)
2
+2(
3
)(1)
=
3−1
3+1+2
3
=
2
4+2
3
=
2
2(2+
3
)
=2+
3
Answered by
3
Answer:
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