Which of following is equivalent to (2+1)3-1(2-1)3+1?

Question

Which of following is equivalent to  \frac{(√2+1)^{1-√3}}{(√2-1)^{1+√3}} ?

A. 1
B. √2
C. 3 - 2√2
D. 3 + 2√2
E. 6√2

MathRevolution · Accepted Answer

=>

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

Therefore, the answer is D. 
Answer: D

chetan2u · Answer

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

Multiply both the denominator and numerator of the fraction by (√2+1)
= (\frac{(√2+1)(√2+1)}{(√2-1)(√2+1)})^{√3} = (\frac{(√2+1)(√2+1)}{2-1})^{√3}=(√2+1)^2=2+1+2\sqrt{2}=3+2\sqrt{2} ..

D

Kinshook · Answer

Asked:  Which of following is equivalent to  \frac{(√2+1)^{√3-1}}{(√2-1)^{√3+1}} ?

\frac{(√2+1)^{√3-1}}{(√2-1)^{√3+1}} 
Multiplying both numerator and denominator by  (√2+1)^{√3+1} 
 \frac{(√2+1)^{√3-1}(√2+1)^{√3+1}}{(√2-1)^{√3+1}(√2+1)^{√3+1}} 
 (√2+1)^{√3-1+√3+1} 
 (√2+1)^{2√3}

None of the answer choice match this.
Please correct me if I am wrong.

Kinshook · Answer

Why {1-√3} is taken when {√3-1} is given in the question?

With this question will have correct answer choices.

amarsinha · Answer

The answer comes out to be (3+2(sqrt 2))**sqrt(3). which is not any of the option.

Bunuel · Answer

You are right. Correct question reads:

Which of following is equivalent to  \frac{(√2+1)^{1-√3}}{(√2-1)^{1+√3}} ?

Edited. Thank you.

Kinshook · Answer

Asked:  Which of following is equivalent to  \frac{(√2+1)^{1-√3}}{(√2-1)^{1+√3}} ?

\frac{(√2+1)^{1-√3}}{(√2-1)^{1+√3}} 
Multiplying both numerator and denominator by  (√2+1)^{1+√3} 
 \frac{(√2+1)^{1-√3}(√2+1)^{1+√3}}{(√2-1)^{1+√3}(√2+1)^{1+√3}} 
 (√2+1)^{1-√3+1+√3} 
 (√2+1)^{2} 
 (3+2√2)

IMO D

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Which of following is equivalent to (2+1)3-1(2-1)3+1?

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Which of following is equivalent to (2+1)3-1(2-1)3+1?

Prep Toolkit

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