I f space space a space equals fraction numerator 1 over denominator 7 minus 4 square root of 3 end fraction space a n d space space b equals fraction numerator 1 over denominator 7 plus 4 square root of 3 end fraction space space comma space f i n d space t h e space v a l u e space space o f space 1 right parenthesis space a squared plus b to the power of 2 to the power of blank end exponent space comma space 2 right parenthesis space a cubed plus b cubed

Asked by kishor.kp14 | 21st Jun, 2019, 02:06: PM

Expert Answer:

begin mathsize 16px style straight a space equals space fraction numerator 1 over denominator 7 space minus space 4 square root of 3 end fraction space and space straight b space equals space fraction numerator 1 over denominator 7 space plus space 4 square root of 3 end fraction
straight a space equals space fraction numerator 1 over denominator 7 space minus space 4 square root of 3 end fraction cross times space fraction numerator 7 space plus space 4 square root of 3 over denominator 7 space plus space 4 square root of 3 end fraction space space space space space space space space space space space space space..... space Rationalising
space space space equals space fraction numerator 7 space plus space 4 square root of 3 over denominator 7 squared space minus space open parentheses 4 square root of 3 close parentheses 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 space space space space space
space space space equals space fraction numerator 7 space plus space 4 square root of 3 over denominator 49 space minus space 48 end fraction
space space space equals space 7 space plus space 4 square root of 3 space space
straight b space equals space fraction numerator 1 over denominator 7 space plus space 4 square root of 3 end fraction cross times space fraction numerator 7 space minus space 4 square root of 3 over denominator 7 space minus space 4 square root of 3 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 space space space space..... space Rationalising
space space space equals space fraction numerator 7 space plus space 4 square root of 3 over denominator 7 squared space minus space open parentheses 4 square root of 3 close parentheses 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 space space space space space space space space space space space space space space space... space since left parenthesis straight a space minus space straight b right parenthesis space left parenthesis straight a space plus space straight b right parenthesis space equals space straight a squared space minus space straight b squared
space space space equals space fraction numerator 7 space minus space 4 square root of 3 over denominator 49 space minus space 48 end fraction
space space space equals space 7 space minus space 4 square root of 3 space space space space
1 right parenthesis
straight a squared plus space straight b squared space equals space left parenthesis straight a space plus space straight b right parenthesis squared minus space 2 ab
space space space space space space space space space space space space space equals open parentheses 7 space plus space 4 square root of 3 space plus space 7 space minus space 4 square root of 3 close parentheses squared space space minus space 2 space cross times open parentheses 7 space plus space 4 square root of 3 close parentheses open parentheses 7 space minus space 4 square root of 3 close parentheses
space space space space space space space space space space space space space equals 14 squared space minus space 2 left parenthesis 49 space minus space 48 right parenthesis
space space space space space space space space space space space space space equals 196 minus space 2
space space space space space space space space space space space space space equals 194 space space
2 right parenthesis
straight a cubed plus space straight b cubed space equals space left parenthesis straight a space plus space straight b right parenthesis cubed minus space 3 ab open parentheses straight a space plus space straight b close parentheses
space space space space space space space space space space space space equals space open parentheses 7 space plus space 4 square root of 3 space plus space 7 space minus space 4 square root of 3 close parentheses cubed space minus space 3 space cross times space open parentheses 7 space plus space 4 square root of 3 close parentheses open parentheses 7 space plus space 4 square root of 3 close parentheses open parentheses space 7 space plus space 4 square root of 3 plus space space 7 space minus space 4 square root of 3 close parentheses
space space space space space space space space space space space space equals space 14 cubed space minus space 3 left parenthesis 49 space minus space 28 right parenthesis left parenthesis 14 right parenthesis
space space space space space space space space space space space space equals space 2744 space minus space 42
space space space space space space space space space space space space equals space 2702
end style

Answered by Yasmeen Khan | 21st Jun, 2019, 05:16: PM