Question

If $\frac{3 + √5}{2√5 + 3}$ = a + b√5, find the values of rational numbers a and b.

Answer 1

Answer:

PLZ MARK ME AS BRAINIST

Step-by-step explanation:

LHS=(3-√5)/(3+2√5)

=[(3-√5)/(3√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 you.

:)

Answer 2

Answer:

a=1/11 and b=3/11

Step-by-step explanation:

$\frac{3 + \sqrt{5} }{2 \sqrt{5} + 3} = a + b \sqrt{5} \\ \frac{3 + \sqrt{5} }{2 \sqrt{5} + 3} \times \frac{2 \sqrt{5} - 3}{2 \sqrt{5} - 3} = a + b \sqrt{5} \\ \frac{(3 + \sqrt{5} )(2 \sqrt{5} - 3)}{(2 \sqrt{5} )^{2} - (3)^{2} } = a + b \sqrt{5} \\ \frac{6 \sqrt{5} - 9 + 10 - 3 \sqrt{5} }{20 - 9} = a + b \sqrt{5} \\ \frac{3 \sqrt{5} + 1 }{11} = a + b \sqrt{5} \\ \frac{1}{11} + \frac{3 \sqrt{5} }{11} = a + b \sqrt{5} \\ a = \frac{1}{11}. \: \: \: \: \: b = \frac{3}{11} .$