wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If x = 3+2√2 , find the value of (√x - 1/√x)

Open in App
Solution

x = 3 + 2√2
youcan write as
x = 2 + 1 + 2√2
x = (√2)² + 1² + 2(√2)(1)
use a squared plus b squared plus 2 a b equals left parenthesis a plus b right parenthesis squared
where a=√2 and b=1
now you can write as
x = (√2)² + 1² + 2(√2)(1) =left parenthesis square root of 2 plus 1 right parenthesis squared
t a k i n g space b o t h space s i d e space r o o t square root of x equals square root of 2 plus 1
we have find






left parenthesis � x space minus space fraction numerator 1 over denominator square root of x end fraction right parenthesis equals left parenthesis � 2 space plus space 1 right parenthesis minus fraction numerator 1 over denominator left parenthesis � 2 space plus space 1 right parenthesis end fraction equals left parenthesis � 2 space plus space 1 right parenthesis minus left parenthesis fraction numerator 1 over denominator left parenthesis � 2 space plus space 1 right parenthesis end fraction cross times fraction numerator left parenthesis � 2 space minus space 1 right parenthesis over denominator left parenthesis � 2 space minus space 1 right parenthesis end fraction right parenthesis space space space space space space space space space left square bracket m u l t i p l y space a n d space d i v i d e space b y left parenthesis � 2 space minus space 1 right parenthesis right square bracket equals left parenthesis � 2 space plus space 1 right parenthesis minus fraction numerator left parenthesis � 2 space minus space 1 right parenthesis over denominator left parenthesis � 2 right parenthesis squared space minus space 1 squared end fraction space space space space space space space space space space space space space space space space space space space space space space space space left square bracket u s e space left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis equals a squared minus b squared right square bracket equals left parenthesis � 2 space plus space 1 right parenthesis space minus fraction numerator left parenthesis � 2 space minus space 1 right parenthesis over denominator 2 minus 1 end fraction equals left parenthesis � 2 space plus space 1 right parenthesis space minus left parenthesis � 2 space minus space 1 right parenthesis equals � 2 space plus space 1 space space minus � 2 space plus space 1 equals 2

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebraic Identities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon