यदि `a=(2-sqrt(5))/(2+sqrt(5))` तथा `b=(2+sqrt(5))/(2-sqrt(5))`, तो `a^(2)-b^(2)` का मान ज्ञात करें।

Explanation

`a=(2-sqrt(5))/(2+sqrt(5))=(2-sqrt(5))/(2+sqrt(5))xx(2-sqrt(5))/(2-sqrt(5))=((2-sqrt(5))^(2))/(2^(2)-(sqrt(5))^(2))`
`=(4+5-4sqrt(5))/(4-5)=(9-4sqrt(5))/(-1)=-9+4sqrt(5)`
उसी तरह, `b=-(9+4sqrt(5))`
`therefore a+b=(-9+4sqrt(5))+(-9-4sqrt(5))=-18`
तथा `a-b=(-9+4sqrt(5))-(-9-4sqrt(5))=8sqrt(5)`
अतः, `a^(2)-b^(2)=(a+b)(a-b)=-18xx8sqrt(5)=-144sqrt(5)`