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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 - ICSE Class 10 - Mathematics

Question

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+ z

Solution

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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Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 8

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Solution 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 Concept: Proportions.
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