Question

3+ square root 2 /3 minus root 2=a + b square route 2 find the values of a and b

Answer 1

Hi ,

( 3 + √2 ) / ( 3 - √2 ) = a + b√2

LHS = ( 3 + √2 ) / ( 3 - √2 )

= [ (3 + √2 )² ] / [ ( 3-√2 ) ( 3 + √2 ) ]

= [ 3² + 2×3×√2 + (√2)²] / ( 3² - ( √2 )²]

= ( 9 + 6√2 + 2 ) / ( 9 - 2 )

= ( 11 + 6√2 ) / 7

= ( 11/7 ) + ( 6/7 ) × √2


Now ,

LHS = RHS

( 11/7 ) + ( 6/7 ) ×√2 = a + b√2

Compare both sides, we get

a = 11/7 ;

b = 6/7 ;

I hope this helps you.

:)

Answer 2

Answer:

3+square root 2 /3-square root 2 =a+b square root 2

=> (3+2®)/(3-2®) = a+b 2®

=> (3+2®)×(3+2®)/(3-2®)×(3+2®) = a+b 2®

=> (3+2®)² / (3)²- (2®)² = a+b 2®

=> 3²+2×3×2®+(2®)² / 9-2 = a+b 2®

=> 9+6 2®+2 /7 = a+b 2®

=> 11+6 2®/7 = a+b 2®

=> 11/7+6/7 2® = a+b 2®

=> a=11/7 & b=6/7

I hope this is helpful.....