Question

please give me the answer step by step...​

Answer 1

Answer :

1) -√2(√3 + √2 + 1)/4

2) 254

Solution :

1) Please refer to the attachment

2) • Given : a = 8 + 3√7 , b = 1/a

• To find : a² + b² = ?

We have ;

=> b = 1/a

=> b = 1/(8 + 3√7)

=> b = (8 - 3√7) / (8 + 3√7)•(8 - 3√7)

=> b = (8 - 3√7) / [ 8² - (3√7)² ]

=> b = (8 - 3√7) / (64 - 63)

=> b = (8 - 3√7) / 1

=> b = 8 - 3√7

Now ,

=> (a + b)² = a² + b² + 2ab

=> a² + b² = (a + b)² - 2ab

=> a² + b² = (8 + 3√7 + 8 - 3√7)² - 2a•(1/a)

=> a² + b² = 16² - 2

=> a² + b² = 256 - 2

=> a² + b² = 254

Hence ,

a² + b² = 254