Question

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Answer 1

Answer:

by multiply and divide with its conjugate we can get the number whose denominator is rationalise...

Answer 2

Answer:

Proved!

Step-by-step explanation:

Given Problem:

Prove that 1/2+√3+2/√ 5-√3+1/2-√5 = 0

Solution:

To Prove:

1/2+√3+2/√ 5-√3+1/2-√5 = 0

Method:

a) $\dfrac{1}{2+\sqrt{3} }$

$\dfrac{2- \sqrt{3} }{\ [(2+\sqrt{3) (2-\sqrt{3)]} } }$

$\dfrac{(2-\sqrt{3)} }{[4 - 3]}$

= 2 - √3 -----------(Equation1)

b) $\dfrac{2}{\sqrt{5}-\sqrt{3}  }$

$\dfrac{2(\sqrt{5} + \sqrt{3)} }{(5-3)}$

$\dfrac{2(\sqrt{5} + \sqrt{3} }{(5-3)}$

$\dfrac{2(\sqrt{5} + \sqrt{3}}{2}$

= √5 + √3 ----------(Equation)2

c) $\dfrac{1}{2- \sqrt{5} }$

$\dfrac{2=\sqrt{5} }{[(2-\sqrt{5)(2+\sqrt{5)]} } }$

$\dfrac{2+\sqrt{5} }{4-5}$

√= - ( 2 + √5 ) ---- Equation(3)

According to the Given Problem,

(1) + (2) + (3)

= 2 - √3 + √5 + √3 - ( 2 + √5 )

= 2 - √3 + √5 + √3 - 2 - √5

= 0

Hence Proved!