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Which of the following is equal to 1/(√3−√2)^2?

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Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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New post 03 Jan 2017, 18:32
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E

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Which of the following is equal to \(1/(√3−√2)^2\)?

A) 1

B) 5

C) √6

D) 5 - √6

E) 5 + 2√6

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Re: Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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New post 03 Jan 2017, 19:52
\(\frac{1}{(√3−√2)^2}\)=\(\frac{1*(√3+√2)^2}{(√3−√2)^2*(√3+√2)^2}\) ......multiply denominator and numerator by \((√3+√2)^2\)

=\(\frac{(√3)^2−2(√2)(√3)+(√2)^2}{(√3^2−√2^2)^2}\)

=\(3-2√6+2\)

=\(5+2√6\)


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Re: Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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New post 04 Jan 2017, 12:57
By Simplifying=> 1/(5-2sqrt6)
By rationalising=>(5+2sqrt6)/(25-24)
=>5+2sqrt6

E.

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Re: Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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New post 04 Jan 2017, 18:56
\(1/((√3−√2)^2)=1/(3+2−2√3 √2)=1/(5−2√6)*((5+2√6))/((5−2√6)(5+2√6))=((5+2√6))/(5^2−〖(2√(6))〗^2 )=((5+2√6))/(25−24)=5+√6\)
The answer is E.

Answer: E
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Which of the following is equal to 1/(√3−√2)^2?  [#permalink]

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New post 05 Aug 2018, 19:03
1
MathRevolution wrote:
Which of the following is equal to \(1/(√3−√2)^2\)?

A) 1

B) 5

C) √6

D) 5 - √6

E) 5 + 2√6

I. Simplify and rationalize
Simplify:
\(\frac{1}{(√3−√2)^2}\)
\(\frac{1}{(√3−√2)(√3−√2)}\)
\(\frac{1}{3-2√6+2}=\frac{1}{5-2√6}\)

Rationalize with conjugate: \(5+2√6\)
\((\frac{1}{5-2√6}*\frac{5+2√6}{5+2√6})=\frac{5+2√6}{25-(4*6)}\)

\(\frac{5+2√6}{25-24}=\frac{5+2√6}{1}=5+2√6\)

Answer E

Rationalize all at once
The denominator has two "copies" of \((a-b)\), one of the factored terms of a difference of perfect square \((a+b)(a-b)=a^2-b^2\).

If we multiply by two copies of \((a+b)\) -- the conjugate of the denominator, squared -- we will create two differences of perfect squares that in this instance are integers.

\(\frac{1}{(√3−√2)^2}=\frac{1}{(√3−√2)(√3−√2)}\)

\(\frac{1}{(√3−√2)(√3−√2)}*\frac{(√3+√2)^2}{(√3+√2)^2}\)

\(\frac{1}{(√3−√2)(√3−√2)}*\frac{(√3+√2)(√3+√2)}{(√3+√2)(√3+√2)}\)

\(\frac{(√3+√2)(√3+√2)}{(√3−√2)(√3+√2)(√3−√2)(√3+√2)}\)

\(\frac{3+2√6+2}{(3-2)(3-2)}=\frac{5+2√6}{(1*1)}=5+2√6\)

Answer E
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Which of the following is equal to 1/(√3−√2)^2? &nbs [#permalink] 05 Aug 2018, 19:03
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