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प्रश्न
If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x2+ y2 and y2+ z2
उत्तर
Since y is the mean proportion between x and z
Therefore, y2=xz
Now, we have to prove that xy+yz is the mean proportional between x2+y2 and y2+z2.
(xy + yz)2 = (x2 + y2)(y2 + z2)
LHS = (xy + yz)2
= [y (x + z)]2
= y2(x + z)2
= xz (x + z)2
RHS = (x2 + y2)(y2 + z2)
= (x2 + xz) (xz+ z2)
= x (x + z) z (x + z)
= xz (x + z)2
LHS = RHS
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