Question

5. The difference between two numbers is 48 and the
difference between the arithmetic mean and the geo-
metric mean is two more than half of 1/3 of 96. Find
the numbers.​

Answer 1

Step-by-step explanation:

$(a - b) = 48$ -----(1)

$\frac{(a + b)}{2} - √ab = 96 × \frac{1}{3} × \frac{1}{2} + 2$

$\frac{(a + b - 2√ab)}{2}=18$

$(a + b - 2√ab) = 36$

$(a + b) = 2√ab + 36$ ----(2)

$From \: eq.(1) + eq.(2)$

$2a = 2√ab + 84$

$a = √ab + 42$

$(a - 42)= √a(a-48)$

$(a - 42)² = a(a - 48)$

$a² - 84a + 1764 = a² - 48a$

$-48a + 84a = 1764$

$36a = 1764$

$a = 49$

$then , b = 1$

$The \: numbers \: are \: 49 \: and \: 1.$

Answer 2

Answer:

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✒ The difference between two numbers is 48, the difference between the arithmetic mean and the geometric mean of the numbers is 18. Find the numbers...

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In the attachment.....

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