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Q.

If 2 =1.4142,   then of the following is the value of the expression 2 −1 2 +1 ?  


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a

2.4142

b

5.8282

c

0.4142

d

0.1718 

answer is C.

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Detailed Solution

The given expression is,
2 −1 2 +1  
Now, after multiplying the numerator and denominator by 2 −1 ,   we have,
2 −1 2 +1 = 2 −1 2 +1 × 2 −1 2 −1   ⇒ ( 2 −1) 2 ( 2 ) 2 − (1) 2   ⇒ ( 2 −1) 2 2−1   ⇒ ( 2 −1) 2   ⇒ 2 −1  
Put the value of 2 =1.4142.   ⇒ 2 −1=1.4142−1 ⇒0.4142    Therefore, the value of the given expression 2 −1 2 +1  is 0.4142.  
Hence, option (3) is correct.
 
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