Question

║⊕QUESTION⊕║
‘Obvious’ is the most dangerous word in mathematics.
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CLASS 11
SEQUENCES AND SERIES
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The difference of two numbers is 4 and A.M. between them is 6. Find the numbers.

Answer 1

Step-by-step explanation:

let the two numbers be x and y

x - y = 4........(1)

A.M =>

$\frac{x + y}{2} = 6 \\ x + y = 12.......(2)$

$from \: (1) \: and \: (2) = > \\ 2x = 16 \\ x = 8 \\ \\ put \: x = 8 \: in \: (2) \\ x + y = 12 \\ y = 12 - 8 \\ y = 4$

Hope it helps uh dearie

Answer 2

$\large\underline{ \underline{ \sf \: Solution : \: \: \: }}$

Let ,

$\star$The two numbers are a and b

By the given condition ,

$\star \sf \: \: a - b = 4 \: - - - - \: (i) \\ \\ \star \sf \: \: </p><p> \frac{a + b }{2} = 6 \: - - - - \: (ii)$

Add Equation (i) and (ii) , we get

$\sf \implies (a - b) + (a + b) = 4 + 12 \\ \\ \sf \implies</p><p>2a = 16 \\ \\ \sf \implies</p><p>a = 8</p><p>$

Put the value of a = 8 in eq (i)

$\sf \implies a - b = 4 \\ \\ \sf \implies </p><p>8 - b = 4 \\ \\ \sf \implies </p><p>- b = 4 - 8 \\ \\ \sf \implies </p><p>b = 4$

$\therefore$The required values are 8 and 4

$\large\underline{ \underline{ \sf \: Remember : \: \: \: }}$

$\huge{ \star} \: \large \fbox{ \fbox{ \sf \: \: Arithmetic \: mean = \frac{ \: \: a + b \: \: }{ 2 } \: \: }}$