If x,y,z are in continued proportion prove-:.....Question is given in picture question no.20.....Thnk u
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since , x , y , z are in continued proportion
hence , x : y :: y : z
=> x/y = y/z
=> y² = xz
LHS = (x+y)² / (y+z)²
=> (x²+y²+2xy) / (y²+z²+2yz)
=> (x²+xz+2xy) / (xz+z²+2yz). (as , y² = xz)
=> x (x+z+2y) / z (x+z+2y)
(x+z+2y) gets cancelled out
=> x / z
RHS = x / z
since , LHS = RHS
Proved
hope this helps
hence , x : y :: y : z
=> x/y = y/z
=> y² = xz
LHS = (x+y)² / (y+z)²
=> (x²+y²+2xy) / (y²+z²+2yz)
=> (x²+xz+2xy) / (xz+z²+2yz). (as , y² = xz)
=> x (x+z+2y) / z (x+z+2y)
(x+z+2y) gets cancelled out
=> x / z
RHS = x / z
since , LHS = RHS
Proved
hope this helps
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