Question

a, b are positive. If a,x,b are in A.P. and if a, y, z ,b are in G.P. , then y^3+z^3/ xyz

Answer 1

value of (y³ + z³)/xyz is 2.

given, a , b are positive and a , x , b are in Arithmetic progression.

i.e., x - a = b - x

⇒x = (a + b)/2 ...........(1)

again a, y, z, b are in Geometric progression.

so, y/a = z/y = b/z

y² = az ........(2) , z² = by ........(3)

and yz = ab..........(4)

now (y³ + z³)/xyz

= {y².y + z².z}/x.yz

= {az.y + by.z}/xyz [ from equations (2) and (3) ]

= yz(a + b)/xyz

= (a + b)/x

= (a + b)/{(a + b)/2} [ from equation (1)]

= 2

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