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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. - Mathematics

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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`

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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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(B) | Q: 9 | Page no. 94

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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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