Question

If x : y : : y : z, prove that x : z = x2 : y2

Answer 1

Let, x : y = y : z = k

.'. y = k. z ................... (1)

.'. x = k. y

= k²z. [we get this from equation 1]

.'. L. H. S = x : z

= k²z : z [Previously proved]

= k²

= (x)² : (y)2. [As, x : y = k]

= x² : y²

= R.H.S

.'. x : z = x² : y² [PROVED]

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