Question

if a= 5 + 2 root 6 and b=1/a then what will be the value of a2 + b2

Answer 1

Heya,

Here's your answer,

Given,

a = 5+2√6
b = 1/a

Now,

1 / (5 + 2√6)

( 5 - 2 √6 ) / (5 + 2√6) (5 - 2√6)

5 - 2√6 / [5² - 2√6]²

( 5 - 2 √6 ) / ( 25 -24 )

( 5 - 2 √6 )

Then,

By using formula, a² + b² = (a + b)² - 2ab

(5 + 2√6 + 5 - 2 √6 )² - 2 (5 + 2√6) (5-2√6)

(10)² - 2 (25 - 24) =>> 100 - 2 = 98

a² + b² = 98!!

Hope this will help you!! :)

Answer 2

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Given,

a = 5+2√6

b = 1/a

Now,

1 / (5 + 2√6)

( 5 - 2 √6 ) / (5 + 2√6) (5 - 2√6)

5 - 2√6 / [5² - 2√6]²

( 5 - 2 √6 ) / ( 25 -24 )

( 5 - 2 √6 )

Then,

By using formula, a² + b² = (a + b)² - 2ab

(5 + 2√6 + 5 - 2 √6 )² - 2 (5 + 2√6) (5-2√6)

(10)² - 2 (25 - 24) =>> 100 - 2 = 98

a² + b² = 98!!

HOPE SO IT WILL HELP.....