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If `y` is the mean proportional between `x` and `z`, show that `xy + yz` is the mean proportional between x^(2) + y^(2) and y^(2) + z^(2).

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ICSE-RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)-Exercise 7(B)
  1. Find the fourth proportional to : (i) 1.5, 4.5 and 3.5 (ii) 3...

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  2. Find the third proportional to : (i) 2(2)/(3) and 4 (ii) a - b...

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  3. Find the mean proportional between : (i) 6 + 3sqrt(3) and 8 - 4sqr...

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  4. If x + 5 is the mean proportion between x + 2 and x + 9: find the valu...

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  5. If x^(2), 4 and 9 are in continued proprotion, find x.

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  6. What number must be added to each of the numbers 6, 15, 20 and 43 to m...

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  7. (i) If a, b, c are in continued proportion, show that : (a^(2) + b^(2)...

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  8. What least number must be subtracted from each of the numbers 7, 17 an...

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  9. If y is the mean proportional between x and z, show that xy + yz is th...

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  10. If q is the mean proportional between p and r, show that : pqr (p ...

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  11. If three quantities are in continued proportion, show that the ratio o...

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  12. If y is the mean proportional between x and z, prove that : (x^(2) - ...

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  13. Given four quantities a, b, c and d are in proportion. Show that : ...

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  14. Find two numbers such that the mean proportional between them is 12 an...

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  15. Find the third proportional to (x)/(y) + (y)/(x) and sqrt(x^(2) + y^(2...

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  16. If p : q = r : s, then show that : mp + nq : q = mr + ns : s.

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  17. If p+r=mq and (1)/(q)+(1)/(s)=(m)/(r ), then prove that : p:q=r:s .

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