Solve this:- <br />If x and y be unequal and x:y is the duplicate ratio of x+z and y+z , prove that z is the mean proportional between x and y (PLZZZ ANSWER ONLY THOSE WHO KNOW THE ANSWER)
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hey
here is ur answer
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x : y is the duplicate ratio of x + z and y+ z
Therefore x:y = (x+z)2:(y+z)2
x/y = (x+z)2/(y+z)2
x(y+z)2 = y(x+z)2
x(y2 + z2 + 2yz) = y(x2 + z2 + 2xz)
xy2 + xz2 + 2xyz = yx2 + yz2 + 2xyz
xy2 + xz2 = yx2 + yz2
xy2 - yx2 = yz2 - xz2
xy(y - x) = z2(y-x)
y ≠ x because given x and y are unequal in the problem.
Therefore xy = z2
Therefore z is mean proportional between x and y.
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I hope this will help
#Prem✌✌✌
here is ur answer
===========
x : y is the duplicate ratio of x + z and y+ z
Therefore x:y = (x+z)2:(y+z)2
x/y = (x+z)2/(y+z)2
x(y+z)2 = y(x+z)2
x(y2 + z2 + 2yz) = y(x2 + z2 + 2xz)
xy2 + xz2 + 2xyz = yx2 + yz2 + 2xyz
xy2 + xz2 = yx2 + yz2
xy2 - yx2 = yz2 - xz2
xy(y - x) = z2(y-x)
y ≠ x because given x and y are unequal in the problem.
Therefore xy = z2
Therefore z is mean proportional between x and y.
==========
I hope this will help
#Prem✌✌✌
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