If p and q are numbers and `sqrt(p) + sqrt(q) = 2x` then find x

If p and q are distinct primes and xxDelta = |(sqrt(pq),p i,q+sqrt(pq)),(psqrt(q),sqrt(p)+psqrt(p)i,qsqrt(p)+sqrt(p) qi),(qsqrt(p), sqrt(p)+psqrt(q)i,qsqrt(q)+p i)|xx

Let x=sqrt(3-sqrt(5)) and y=sqrt(3+sqrt(5)) If the value of the expression x-y+2x^(2)y+2xy^(2)-x^(4)y+xy^(4) can be expressed in the form sqrt(p)+sqrt(q) where p.q in N, then find the value of (p+q)

If p and q are the intercept on the axis cut by the tangent of sqrt(((x)/(a)))+sqrt(((y)/(b)))=1, prove that (p)/(a)+(q)/(b)=1

If p and q are the intercept on the axis cut by the tangent of sqrt(((x)/(a)))+sqrt(((y)/(b)))=1, prove that (p)/(a)+(q)/(b)=1

If p inR and q = log_(x) (p+sqrt(p^(2)+1)) , then find the value of p in terms of x and q.

If p,q are prime positive integers,prove that sqrt(p)+sqrt(q) is an irrational number.