Question

If x = √7 + √5 and y = √7 - √5, evaluate
i. xy
ii. x^2+y^2

Answer 1

hey here is ur answer

see the attachment above

I hope this helps you

Answer 2

Given That :- x = √7 + √5 & y = √7 - √5

To Find : ( i ) xy & ( ii ) x² + y²

Solution :

( i ) xy

→ xy = ( √7 + √5 ) ( √7 - √5 )

We know that ( a + b ) ( a - b ) = a² - b²

So,

= ( √7 )² - ( √5 )²

= 7 - 5

= 2

( ii ) x² + y²

→ x² + y² = ( √7 + √5 )² + ( √7 - √5 )²

We know that ( a + b )² = a² + 2ab + b² and ( a - b )² = a² - 2ab + b²

Therefore,

( √7 + √5 )² + ( √7 - √5 )²

= [ ( √7 )² + ( 2 × √7 × √5 ) + ( √5 )² ] + [ ( √7 )² - ( 2 × √7 × √5 ) + ( √5 )² ]

= 7 + 2√35 + 5 + 7 - 2√35 + 5

= 24