Question

Choose the correct answers :
if A.M and G.M of two positives numbers a and b are 10 and 8 respectively. Then the values of a and b are
(a)9 and 27
(b)4 and 16
(c)-4 and 16
(d)9 and -27​

Answer 1

Answer:

(b)4 and 16

Step-by-step explanation:

AM of two positives numbers a and b is = (a + b)/2

GM of two positives numbers a and b is = $(ab)^{1/2}$

According to the question:

(a + b)/2 = 10 and $(ab)^{1/2}$ = 8

Now, $(ab)^{1/2}$ = 8

=> ab = $8^2$

=> ab = 64

=> b = 64/a

and (a + b)/2 = 10

=> a + b = 10 × 2

=> a + b = 20

=> a + (64/a) = 20 [as b = 64/a]

=>  $a^{2}$ + 64 = 20a

=>  $a^{2}$ - 20a + 64 = 0

=>  $a^{2}$ - 4a - 16a + 64 = 0

=> a(a - 4) -16(a - 4) = 0

=> (a - 4) ( a - 16) = 0

=> a -4 = 0 or a - 16 = 0

=> a= 4, 16

As b = 64/a

when a = 4 then b = 64/4 = 16

when a = 16 then b = 64/16 = 4

SO (a, b) = (4, 16) or (16, 4)

Answer 2

Answer:

(b) 4 and 16

Step-by-step explanation:

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