`PQ=a/(2b)sqrt((a+b)(3b-a))`

If x = (sqrt(2a + 3b)+sqrt(2a - 3b))/(sqrt(2a + 3b) - sqrt(2a - 3b)) , show that 3bx^(2) - 4ax + 3b = 0 .

sqrt(a/b+b/a-2)= 1) sqrt(a/b)+sqrt(b/a) 2) sqrt(a/b)-sqrt(b/a) 3) sqrt(a)/b-b/sqrt(a) 4) sqrt(a)/b-sqrt(b)/a

Prove that (a^(3/2)+ab)/(ab-b^3)-(sqrt(a))/(sqrt(a)-b)=(sqrt(a))/(b) .

If ((sqrt(a)-sqrt(b))^(2)+4sqrt(ab))/(a-b)=(5)/(3), then the

If x=(sqrt(a+2b)-sqrt(a-2b))/(sqrt((a+2b))+sqrt((a-2b))) , show that bx^(2)-ax+b=0

If PQ be a chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which subtends right angle at the centre then is distance from the centre is equal to (A) (ab)/(sqrt(a^(2)+b^(2)))(B)sqrt(a^(2)+b^(2))(C)sqrt(ab)(D) depends on slope of chord

P and Q are points on the line joining A(-2,5) and B(3,1) such that AP=PQ=QB .Then,the distance of the midpoint of PQ from the origin is (a) 3(b)(sqrt(37))/(2) (b) 4 (d) 3.5