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If the numbers a,x,y,b are in arithmetic...

If the numbers a,x,y,b are in arithmetic progression and the numbers `c^3 , x,y, d^3` are in geometric progression then prove that a+ b = cd ( c+d)

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As `a,x,y,b` are in A.P.,
`:. a+b = x+y ->(1)`
As `c^3,x,y,d^3` are in G.P.,
`:. c^3*y = x^2=> y = x^2/c^3`
and `x*d^3 = y^2=> x = y^2/d^3 => x = x^4/(c^6d^3)`
`=> x^3 = c^6d^3 => x = c^2d`
`:. y = (c^2d)^2/c^3 = cd^2`
Putting value of `x` and `y` in (1),
...
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