Question

1f * 1/(sqrt(5) + sqrt(2)) = a + b * sqrt(10) then find a + b.​

Answer 1

Answer:

$\huge \rm \red{Answer}$

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

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I hope this helps you.

:)