Plzzz answer....Ratio and proportion....Thnx
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since , y is the mean proportional between x and z ,
then ,
x : y :: y : z
=> x/y = y/z
=> xz = y²
LHS = xyz(x+y+z)³
=> LHS = y(xz) (x+y+z)³
=> LHS = y(y)²(x+y+z)³
=> LHS = y³(x+y+z)³
=> LHS = [y(x+y+z)]³
=> LHS = (xy+y²+yz)³
=> LHS = (xy+yz+xz)³ (as , y² = xz)
=> RHS = (xy+yz+zx)³
since , LHS = RHS ,
proved
hope this helps
then ,
x : y :: y : z
=> x/y = y/z
=> xz = y²
LHS = xyz(x+y+z)³
=> LHS = y(xz) (x+y+z)³
=> LHS = y(y)²(x+y+z)³
=> LHS = y³(x+y+z)³
=> LHS = [y(x+y+z)]³
=> LHS = (xy+y²+yz)³
=> LHS = (xy+yz+xz)³ (as , y² = xz)
=> RHS = (xy+yz+zx)³
since , LHS = RHS ,
proved
hope this helps
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