Question

2 - Root 5 / 2 + Root 5 = A Root 5 + B

Answer 1

Answer:

Step-by-step explanation:

Answer:

a²-b²=-144√5

Explanation:

We have ,

i)a=(2-√5)/(2+√5)

Rationalising the denominator,weget

a = \frac{(2-\sqrt{5}))(2-\sqrt{5})}{(2+\sqrt{5})(2-\sqrt{5})}

=\frac{(2-\sqrt{5})^{2}}{2^{2}-(\sqrt{5})^{2}}

= \frac{(4+5-4\times\sqrt{5})}{4-5}

= \frac{(9-4\sqrt{5}}{(-1)} ----(1)

ii) b=(2+√5)/(2-√5)

Rationalising the denominator,we get

b = \frac{(2+\sqrt{5}))(2+\sqrt{5})}{(2-\sqrt{5})(2+\sqrt{5})}

=\frac{(2+\sqrt{5})^{2}}{2^{2}-(\sqrt{5})^{2}}

= \frac{(4+5+4\times\sqrt{5})}{4-5}

= \frac{(9+4\sqrt{5}}{(-1)} ----(2)

iii) a²-b²

=[(9-4√5)/(-1)]²-[

(9+4√5)/(-1)]²

=(9-4√5)²-(9+4√5)²

______________________

Weknow that,

(a-b)²-(a+b)²=-4ab

________________________

=-4×9×4√5

=-144√5