If √2 +√5√2 − √5 = a + b√10, find the values of a and b
Answers
Answered by
36
Hi ,
LHS = (√2 + √5 )/(√2 - √5 )
rationalize the denominator ,
= (√2 + √5 )² / [ (√2 - √5 )(√2 + √5 )]
= [ (√2)² +(√5)² + 2 × √2 × √5 ] /[(√2)² -(√5)²]
= [ 2 + 5 + 2√10 ] / (2 - 5 )
= ( 7 + 2√10 ) / ( - 3 )
= RHS
Therefore ,
(7+2√10 ) / (- 3 ) = a + b√10
7 / ( - 3 ) + ( - 2 / 3 ) × √10 = a + b √10
compare both sides ,
a = - 7/3 ,
b = - 2/ 3
I hope this helps you.
:)
LHS = (√2 + √5 )/(√2 - √5 )
rationalize the denominator ,
= (√2 + √5 )² / [ (√2 - √5 )(√2 + √5 )]
= [ (√2)² +(√5)² + 2 × √2 × √5 ] /[(√2)² -(√5)²]
= [ 2 + 5 + 2√10 ] / (2 - 5 )
= ( 7 + 2√10 ) / ( - 3 )
= RHS
Therefore ,
(7+2√10 ) / (- 3 ) = a + b√10
7 / ( - 3 ) + ( - 2 / 3 ) × √10 = a + b √10
compare both sides ,
a = - 7/3 ,
b = - 2/ 3
I hope this helps you.
:)
Answered by
11
Step-by-step explanation:
a=7/3
b=2/3
HOPE IT HELPS
Attachments:
Similar questions