If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is:
a(b + c)
b(a + c)
c(a + b)
none of these
Ratio Proportion
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Question

If b is the mean proportion between a and c, then the mean proportion between(a^2 + b^2) and (b^2 + c^2) is :(a) a(b + c) (b) b(a + c) (c) c(a + b) (d) none of these

KnowledgeBoat · Accepted Answer

Since b is the mean proportion between a and c, Let the required mean proportion be x. Then, Now substitute b2 = ac: ⇒ x2 = (a2 + b2)(b2 + c2) ⇒ x2 = a2b2 + a2c2 + b4 + b2c2 ⇒ x2 = a2b2 + (ac)2 + b4 + b2c2 ⇒ x2 = a2b2 + (b)2 + b4 + b2c2 ⇒ x2 = a2b2 + b4 + b4 + b2c2 ⇒ x2 = b2(a2 + 2b2 + c2) ⇒ x2 = b2(a2 + 2ac + c2) ⇒ x2 = b2(a + c)2. Therefore, Hence, option 2 is the correct option.

Mathematics

If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is:
a(b + c)
b(a + c)
c(a + b)
none of these

Ratio Proportion

Related Questions

Mathematics

If b is the mean proportion between a and c, then the mean proportion between (a2 + b2) and (b2 + c2) is:a(b + c)b(a + c)c(a + b)none of these

Ratio Proportion

Related Questions

If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is:
a(b + c)
b(a + c)
c(a + b)
none of these