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# If Y is the Mean Proportional Between X and Z; Show that Xy + Yz is the Mean Proportional Between X2+Y2 And Y2+ Z2. - ICSE Class 10 - Mathematics

#### Question

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x2+y2 and y2+ z2.

#### Solution

Since y is the mean proportion between x and z
Therefore, y= xz
Now, we have to prove that xy+yz is the mean proportional between x2+y2 and y2+z2, i.e., (xy + yz)^2 = (x^2 + y^2)(y^2 + z^2)

LHS = (xy + yz)^2

=[y(x + z)]^2

= y^2(x + z)^2

= xz(x + z)^2`

LHS = RHS

Hence, proved.

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7B | Q: 9

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Solution If Y is the Mean Proportional Between X and Z; Show that Xy + Yz is the Mean Proportional Between X2+Y2 And Y2+ Z2. Concept: Proportions.
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