Question

please answer this dont write unwanted answers or it will be reported​

Answer 1

EXPLANATION.

$\sf \implies \dfrac{2 - \sqrt{5} }{2 + \sqrt{5} } \ = a\sqrt{5} + b.$

As we know that,

Rationalize the equation, we get.

$\sf \implies \dfrac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \dfrac{2 - \sqrt{5} }{2 - \sqrt{5} }$

$\sf \implies \dfrac{(2 - \sqrt{5})^{2} }{(2)^{2} - (\sqrt{5} )^{2} } \ = \dfrac{4 + 5 - 2(2)(\sqrt{5} )}{4 - 5}$

$\sf \implies \dfrac{9 - 4\sqrt{5} }{- 1} \ = a\sqrt{5} + b.$

$\sf \implies \dfrac{-(9 + 4\sqrt{5} )}{- 1} \ = a\sqrt{5} + b.$

$\sf \implies \dfrac{9 + 4\sqrt{5} }{ 1} \ = a\sqrt{5} + b.$

$\sf \implies a = 4 \ & \ b = 9.$

Answer 2

Question:-

• If ( 2 - √5 )/( 2 + √5 ) =a√5 + b , then find the value of a and b.

To Find:-

• Find the value of a and b.

Solution:-

$\dashrightarrow\sf \: \dfrac { 2 - \sqrt { 5 } } { 2 + \sqrt { 5 } } = a \sqrt { 5 } + b$

• Rationalise the denominator

$\dashrightarrow\sf \: \dfrac { 2 - \sqrt { 5 } } { 2 + \sqrt { 5 } } \times \dfrac { 2 - \sqrt { 5 } } { 2 - \sqrt { 5 } } = a \sqrt { 5 } + b$

$\dashrightarrow\sf \: \dfrac { { ( 2 - \sqrt { 5 } ) }^{ 2 } } { ( 2 + \sqrt { 5 } )( 2 - \sqrt { 5 } ) } = a \sqrt { 5 } + b$

$\dashrightarrow\sf \: \dfrac { 4 + 5 - 4 \sqrt { 5 } } { 4 - 5 } = a \sqrt { 5 } + b$

$\dashrightarrow\sf \: \dfrac { - ( 9 + 4 \sqrt { 5 } ) } { - 1 } = a \sqrt { 5 } + b$

$\dashrightarrow\sf \: 9 + 4 \sqrt { 5 } = a \sqrt { 5 } + b$

Hence ,

• a = 4 , b = 9