Given that \(p = 1 + \sqrt{2}\) and \(q = 1 - \sqrt{2}\), evaluate \(\frac{p^{2} - q^{2}}{2pq}\).

olaleye8

11 years ago

p=1+2^1/2,q=1-2^1/2

p^2-q^2=(p-q)*(p+q)

={(1+2^1/2)-(1-2^1/2)}*{(1+2^1/2)+(1-2^1/2)}

=2(2^1/2)*2

=2^5/2

2pq=2*(1+2^1/2)*(1-2^1/2)=

2(1-2)=2(-1)=-2

eva. {p^2-q^2}/2pq

" (2^5/2)/-2

-(2^<5/2-1>)

-(2^3/2)=-2^3/2 -D

gloriez

4 months ago

hi