Ratio of Root(3) Terms

Algebra Level 2

What does the following expression evaluate to?

3 + 1 ( 3 + 2 ) ( 3 − 1 ) \large{\frac{\sqrt{3} + 1}{(\sqrt{3} + 2)(\sqrt{3} -1)}}


The answer is 1.

Steven Chase by Steven Chase , 37, USA

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2 solutions

3 + 1 ( 3 + 2 ) ( 3 − 1 ) ⇒ ( 3 + 1 ) ( 3 + 1 ) ( 3 + 2 ) ( 3 − 1 ) ( 3 + 1 ) \frac {\sqrt{3}+1}{(\sqrt{3}+2)(\sqrt{3}-1)} \Rightarrow \frac { (\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}+2)(\sqrt{3}-1)(\sqrt{3}+1)}

= 3 + 2 3 + 1 ( 3 + 2 ) ( 3 − 1 ) = 4 + 2 3 ( 3 + 2 ) ⋅ 2 = \frac {3+2\sqrt{3}+1}{(\sqrt{3}+2)(3-1)} = \frac {4+2\sqrt{3}}{(\sqrt{3}+2) \cdot 2}

= 2 ⋅ ( 3 + 2 ) 2 ⋅ ( 3 + 2 ) = \frac {2\cdot (\sqrt{3}+2)}{2 \cdot (\sqrt{3}+2)}

= 1 = 1

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Did the same way

I Gede Arya Raditya Parameswara - 4 years, 4 months ago
Genis Dude
Feb 10, 2017

Expandind the denominator ,

(√3+2)(√3-1)

→3+2√3-√3-2

→√3+1

Therefore,

denominator and numerator are same

So required answer is 1

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