(ax+b)^(p/q)

If alpha,beta are the roots of ax^(2)+bx+c=0and alpha+h,beta+h are the roots of px^(2)+qx+r=0 thenh =-(1)/(2)((a)/(b)-(p)/(q)) b.((b)/(a)-(q)/(p))c(1)/(2)((b)/(q)-(q)/(p)) d.none of these

In an A.P. the pth and qth terms are respectively a and b. Show that the sum of first p + q terms is (p+q)/2{(a+b)+(a-b)/(p-q)} .

laws of rational exponent (v)(ab)^(p)=a^(p)b^(p)(vi)((a)/(b))^(p)=(a^(p))/(b^(p))(vii)a^((p)/(q))=(a^(p))^((1)/(q))=(a^(q))^((1)/(p))

If the polynomial (ax^(p)+bx^(q)-3) be divided by (x - a) and (x - b), the remainder in both the cases is (-1). Prove that (a^(p+1)-b^(q+1))/(b^(p-1)-a^(q-1))=ab

Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

Prove that a^(p)b^(q)<((ap+bq)/(p+q))^(p+q)

If the tangent at any point on the curve ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1 makes the intercepts, p,q and the axes then (p^(2))/(a^(2))+(q^(2))/(b^(2))=

If the tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 makes intercepts p and q on the coordinate axes, then a^(2)/p^(2) + b^(2)/q^(2) =