Question

if a equal to 2- root 5 by 2+ root 5 and b equal to 2 + root 5 by 2 - root 5 find a square - b square

Answer 1

this is the answer hope it helps

Answer 2

Answer:

a² - b² = -144√5

Explanation:

We have ,

i)a = (2-√5)/(2+√5)

Rationalising the denominator, we get

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

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

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

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

______________________

We know that,

(a-b)² - (a+b)² = -4ab

________________________

= -4×9×4√5

= -144√5