Question

3-root 5/3+2 root 5=a root 5-b

Answer 1

Question:-

3-root 5/3+2 root 5=a root 5-b

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LHS = ( 3 - √5 )/(3 + 2√5 )

= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]

= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]

= ( 9√5 - 19 )/( 20 - 9 )

= ( 9√5 - 19 )/11

= ( 9/11 )√5 - 19/11 ---( 1 )

= a√5 - b ----------( 2 ) [ RHS ]

from ( 1 ) and ( 2 ) ,

a = 9/11 ,

b = 19/11

hope it helps you..

Answer 2

Answer:

3-root 5/3+2 root 5=a root 5-b

LHS = ( 3 - √5 )/(3 + 2√5 )

= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]

= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]

= ( 9√5 - 19 )/( 20 - 9 )

= ( 9√5 - 19 )/11

= ( 9/11 )√5 - 19/11 ---( 1 )

= a√5 - b ----------( 2 ) [ RHS ]

from ( 1 ) and ( 2 ) ,

a = 9/11 ,

b = 19/11

Step-by-step explanation: