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प्रश्न
If y is the mean proportional between x and z; show that xy + yz is the mean proportional 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,
i.e., (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
Hence, proved.
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