Three-numbers-are-in-G-P-such-that-their-sum-is-p-and-the-sum-of-their-square-is-q-Find-the-middle-term-of-the-G-P-

Question Number 55893 by Tawa1 last updated on 05/Mar/19

Three numbers are in G . P such that their sum is p and the

sum of their square is q . Find the middle term of the G . P

Answered by kaivan.ahmadi last updated on 05/Mar/19

l e t a, b, c a r e n u m b e r s, s o

b^{2} = a c .

a + b + c = p \Rightarrow a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c = p^{2} \Rightarrow

q + 2 a b + 2 b^{2} + 2 b c = p^{2} \Rightarrow q + 2 b (a + b + c) = p^{2}

q + 2 b p = p^{2} \Rightarrow b = \frac{p^{2} - q}{2 p}

Commented by Tawa1 last updated on 05/Mar/19

God bless you sir

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