i f space x equals 1 plus square root of 2 comma t h e n space f i n d space t h e space v a l u e space o f space open parentheses x minus 1 over x close parentheses cubed.

Asked by kishor.kp14 | 24th Jun, 2019, 07:50: PM

Expert Answer:

begin mathsize 16px style straight x space equals space 1 space plus space square root of 2
rightwards double arrow 1 over straight x space equals space fraction numerator 1 over denominator 1 space plus space square root of 2 end fraction space cross times space fraction numerator 1 space minus space square root of 2 over denominator 1 space minus space square root of 2 end fraction space space space space space space space space space space space space space space space space space.... space Rationalising space the space denominator
space space space space space space space space space equals space fraction numerator 1 space minus space square root of 2 over denominator 1 squared space minus space open parentheses square root of 2 close parentheses squared end fraction
space space space space space space space space space equals fraction numerator 1 space minus space square root of 2 over denominator 1 space minus space 2 end fraction
space space space space space space space space space equals square root of 2 space minus space 1
rightwards double arrow open parentheses straight x space minus space 1 over straight x close parentheses cubed space equals space open square brackets 1 space plus space square root of 2 space minus open parentheses square root of 2 space minus space 1 close parentheses close square brackets cubed
space space space space space space space space space space space space space space space space space space space space equals open parentheses 1 space plus square root of 2 space minus space square root of 2 space plus space 1 space close parentheses cubed
space space space space space space space space space space space space space space space space space space space space equals space 2 cubed space equals space 8 end style

Answered by Yasmeen Khan | 25th Jun, 2019, 10:17: AM