Math, asked by Tweet639, 1 year ago

If root of 5+root of3=x and root of of 5- root of 3=y then the value of x×x×x×x-y×y×y×y is?

Answers

Answered by mysticd
2
Hi ,

√5 + √3 = x --- ( 1 )

√5 - √3 = y ---- ( 2 ) 

i ) x² + y²  = ( √5 + √3 )² + ( √5 - √3 )²

                = 2[ ( √5 )² + (√3 )² ]

                = 2 ( 5 + 3 )

                = 2 × 8 

                = 16 -----( 3 ) 


ii ) x² - y² = ( √5 + √3 )² - ( √5 - √3 )²

                = 4 × √5 × √3

                = 4√15 ----( 4 )

iii ) according to the problem 

x^4 - y^4 = ( x² + y² ) ( x² - y² )

               = 16 × 4√15  [ from ( 3 ) and ( 4 ) ]

               = 64√15

I hope this helps you.

:)
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