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
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.
:)
√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.
:)
Similar questions