4 divided by 2 + root 7 + root 3
Answers
Step-by-step explanation:
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\begin{gathered} = \frac{4}{2 + \sqrt{3} + \sqrt{7} } \\ \\ = \frac{4}{(2 + \sqrt{3)} + \sqrt{7} } \\ \\ = \frac{4}{(2 + \sqrt{3)} + \sqrt{7} } \times \frac{(2 + \sqrt{3)} - \sqrt{7} }{(2 + \sqrt{3)} - \sqrt{7}} \\ \\= = > \: {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ = \frac{4(2 + \sqrt{3} - \sqrt{7}) }{ {(2 + \sqrt{3}) }^{2} - {( \sqrt{7} )}^{2} } \\ \\ = \frac{4(2 + \sqrt{3} - \sqrt{7})}{4 + 4 \sqrt{3} + 3 - 7} \\ \\ = \frac{4(2 + \sqrt{3} - \sqrt{7})}{4 \sqrt{3} + 7 - 7 } \\ \\ = \frac{4(2 + \sqrt{3} - \sqrt{7})}{4 \sqrt{3} } \\ \\ = \frac{(2 + \sqrt{3} - \sqrt{7})}{ \sqrt{3} } \\ \\ = \frac{(2 + \sqrt{3} - \sqrt{7})}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{2 \sqrt{3} + 3 - \sqrt{21} }{3} \\ \\ \end{gathered}
=
2+
3
+
7
4
=
(2+
3)
+
7
4
=
(2+
3)
+
7
4
×
(2+
3)
−
7
(2+
3)
−
7
==>a
2
−b
2
=(a+b)(a−b)
=
(2+
3
)
2
−(
7
)
2
4(2+
3
−
7
)
=
4+4
3
+3−7
4(2+
3
−
7
)
=
4
3
+7−7
4(2+
3
−
7
)
=
4
3
4(2+
3
−
7
)
=
3
(2+
3
−
7
)
=
3
(2+
3
−
7
)
×
3
3
=
3
2
3
+3−
21
Answer:
4/2+root7+root3
4/2+root 10 is the correct answer
Step-by-step explanation: