Question

if a=√2-1 upon √2+1 and b=√2+1 upon √2-1 then find a square+b square

Answer 1

HELLO DEAR,

$a = \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1} \\ \\ = > a = \frac{2 + 1 - 2 \sqrt{2} }{2 - 1} \\ \\ = > a = 3 - 2 \sqrt{2}$

a² = (3)² + (2√2)² - 2×3(2√2)

=> 9+8-12√2

=> 17-12√2

and

$b = \frac{ \sqrt{2} + 1}{ \sqrt{2} - 1} \times \frac{ \sqrt{2} + 1}{ \sqrt{2} + 1 } \\ \\ = > b = \frac{2 + 1 + 2 \sqrt{2} }{2 - 1} \\ \\ = > b = 3 + 2 \sqrt{2}$

b² = (3)²+(2√2)² + 2×3(2√2)

=> 9+8+12√2

=> 17+12√2

hence,

a²+b² = (17-12√2)+ (17+ 12√2)

=> 17+17+ 2√2- 2√2

=> 34

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hi,

Please see the attached file!


Thanks