Question

find sum of 3 consitive terms of an a,p and find their product of -120find three numvers
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Answer 1

Answer:

Let the number are x−y,x,x+y

Sum =−3

⇒x−y+3x+x+y=−3

⇒3x=−3

⇒x=−1

Now product =8

⇒(x−y)(x)(x+y)=8

Substituting x=−1

we get (−1−y)(−1)(−1+y)=8

(y

2

−1)=8

⇒y=±3

The no : are −4,−1,2 or 2,−1,−

Answer 2

Let the 3 consecutive numbers be a-d, a, and a+d respectively.

where a = first term of the AP and d=is their common difference.

Now given that sun of the three numbers is 6.

So we get =>

a + a-d + a + d = 6

=> 3a = 6

=>a = 2

Also, a(a-d)(a+d) = -9

Putting a = 2 we get =>

2(2-d)(2+d) = -9

By using (a+b)(a-b) = a²-b² we get =>

2(2² - d²) = -9

=> 2(4- d²) = -9

=> 8 -2d² = -17

=>-2d² = -25

=>d² = 25/2

=> d =√(25/2)

Hence the terms are =>

2 - √(25/2),2 and 2 + √(25/2) respectively.

Also we can write the terms as

2 - (5/√2) , 2 and 2 + (5/√2)

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