li mean of'two items is ls and Il.l. is 9. find our their G.M

1.	li mean of'two items is ls and Il.l. is 9. find our their G.M
Answer» Let the two numbers be p and q. Since the arithmetic mean of the two numbers is 16, we take: (p+q)/2 = 16 => p+q = 32 … (1) Now, since the harmonic mean of the two numbers is 9, we have: 2/(1/p + 1/q) = 9 => 2/[(p+q)/pq] = 9=> 2pq/(p+q) = 9 => pq/(p+q) = 9/2 … (2) Now, by placing the value of p+q in equation (2), we take: pq/32 = 9/2 => pq = 9*32/2 … (3) Therefore, the geometric mean of p and q is: sqr(pq) = sqr(144) = 12 Like my answer if you find it useful! hindi ma translation

Answer»

Let the two numbers be p and q. Since the arithmetic mean of the two numbers is 16, we take:

(p+q)/2 = 16 => p+q = 32 … (1)

Now, since the harmonic mean of the two numbers is 9, we have:

2/(1/p + 1/q) = 9 => 2/[(p+q)/pq] = 9=> 2pq/(p+q) = 9 => pq/(p+q) = 9/2 … (2)

Now, by placing the value of p+q in equation (2), we take:

pq/32 = 9/2

=> pq = 9*32/2 … (3)

Therefore, the geometric mean of p and q is:

sqr(pq) = sqr(144) = 12

Like my answer if you find it useful!

hindi ma translation

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