Question

Find the three numbers in Ap whose sum is 9 and product is -165

Answer 1

⠀⠀⠀⠀⠀⠀⠀ANSWER

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 ➺Let the 3 no. be a,b,c

According to question,

a+b+c = 9 and

abc = –165

As they are consecutive numbers which means (Numbers which follow each other in order, without gaps, from smallest to largest)

So,

we can write a, (a+1) , (a+2) as the consecutive numbers

Substituting value in a+b+c=9,

⟹ a+(a+1)+(a+2) = 9

⟹ a+a+a+2+1 = 9

⟹ 3a + 3 =9

⟹ 3a= 9-3

⟹ 3a=6

⟹ a = 2

As a=2 so,

The 2nd no. is = a+1 = 2+1 = 3

The 3rd no. is = a+2 = 2+2 = 4

∴The 3 consecutive number are 2,3,4 ☑

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☆✿╬ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ᴜ╬✿☆

Answer 2

QUESTION:

Find the 3 numbers in AP whose sum is 9 and product is - 165.

SOLUTION:

let the 3 numbers be x, y, z

$x + y+ z= 9$

$xyz = ( - 165)$

x, y, z are in AP,

Therefore,

x=a-d

y=a

z=a+d

Where d is the common difference,

x +y+ z =9

$a - d + a + a+ d = 9$

$3a = 9$

$a = 3$

$xyz = ( - 165)$

$(a - d)(a)(a + d) = ( - 165)$

$(a)( {a}^{2} - {d}^{2} ) = ( - 165)$

$3(9 - {d}^{2} ) = ( - 165)$

$(9 - {d}^{2} ) = ( - 55)$

${d}^{2} = 64$

$d = 8 \: or \: d = ( - 8)$

For d=8, the numbers are:

x=a-d=3-8=-5

y=a=3

z=a+d=3+8=11

(-5),3,11

For d=(-8),the numbers are:

x=a-d=3-(-8)=11

y=a=3

z=a+d=3+(-8)=-5

11,3,(-5)

Hope this helps you..!! ❤️