If a=1+√2+√3 and b=1+√2-√3 find a square +b square -2a-2b

Asked by Payalagrawal78 | 10th May, 2019, 08:18: AM

Expert Answer:

begin mathsize 16px style If space straight a equals 1 plus √ 2 plus √ 3 space and space straight b equals 1 plus √ 2 minus √ 3 space find space straight a space square space plus straight b space square space minus 2 straight a minus 2 straight b

To space find colon space straight a squared space plus space straight b squared space minus space 2 straight a space minus space 2 straight b space equals straight a squared space plus space straight b squared space minus space 2 open parentheses straight a space plus space straight b close parentheses

straight a squared space equals space open square brackets open parentheses 1 close parentheses space plus space open parentheses square root of 2 plus square root of 3 close parentheses close square brackets squared space
space space space space space equals space 1 squared space plus space 2 space open parentheses square root of 2 plus square root of 3 close parentheses space plus space space open parentheses square root of 2 plus square root of 3 close parentheses squared
space space space space space equals space 1 space plus space 2 square root of 2 space space plus space 2 square root of 3 space plus space 2 space plus space 3 space plus space 2 square root of 6
space space space space space equals space 6 plus space 2 square root of 2 space space plus space 2 square root of 3 space plus space 2 square root of 6 space space space.... left parenthesis straight i right parenthesis
space space space space space
straight b squared space equals space open square brackets open parentheses 1 close parentheses space plus space open parentheses square root of 2 minus square root of 3 close parentheses close square brackets squared space
space space space space space equals space 1 squared space plus space 2 space open parentheses square root of 2 space minus square root of 3 close parentheses space plus space space open parentheses square root of 2 minus square root of 3 close parentheses squared
space space space space space equals space 1 space plus space 2 square root of 2 space space minus space 2 square root of 3 space plus space 2 space plus space 3 space minus space 2 square root of 6
space space space space space equals space 6 space plus space 2 square root of 2 space space minus space 2 square root of 3 space minus space 2 square root of 6 space space space space space space space.... space left parenthesis straight i right parenthesis
straight a space plus space straight b space equals 1 space plus space square root of 2 plus square root of 3 space plus 1 space plus space space square root of 2 minus square root of 3
space space space space space space space space space space space space equals space 2 space plus space 2 square root of 2 space space space space space space space space space space space.... left parenthesis iii right parenthesis
From space space space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get

straight a squared space plus space straight b squared space minus space 2 open parentheses straight a space plus space straight b close parentheses space equals space 6 space plus space 2 square root of 2 space space plus space 2 square root of 3 space plus space 2 square root of 6 space plus 6 space plus space 2 square root of 2 space space minus space 2 square root of 3 space minus space 2 square root of 6 space minus space 4 minus 4 square root of 2
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 space 12 space minus space 4
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 8 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 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 space space space space space space space space space space space space space space space space space space space space space space end style

Answered by Yasmeen Khan | 10th May, 2019, 10:06: AM