Question

3-√5/3+2√5=a√5-b
find the value of a and b​

Answer 1

Answer:

a = 9/11

b = 19/11

Step-by-step explanation:

Hi ,

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

I hope this helps

: )

Answer 2

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$= 3 - \sqrt{ \frac{5}{3} } + 2 \sqrt{5} = a \sqrt{5} - b \\ = 3 + \frac{ 5\sqrt{5} }{3} = \sqrt{5a } - b \\ = - \sqrt{5a} = - b - 3 - \frac{5 \sqrt{5} }{3} \\ = a = \frac{b}{ \sqrt{5} } + \frac{3}{ \sqrt{5} } + \frac{5}{3} \\ = a = \frac{b \sqrt{5} }{5} + \frac{ 3\sqrt{5} }{5} + \frac{5}{3} \\ = a = \frac{b \sqrt{5} + 3 \sqrt{5} }{5} + \frac{5}{3}$

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