Question

The sum of 3 terms in A. P.is - 3 and their product is 8, then sum of squares of the numbers is
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Answer 1

Answer:-

Let the three terms be a - d , a , a + d.

Given:

sum of the numbers = - 3

→ a - d + a + a + d = - 3

→ 3a = - 3

→ a = - 3/3

→ a = - 1

Also,

Product of the numbers = 8

→ (a - d) * (a) * (a + d) = 8

Putting the value of a and using (a + b) * (a - b) = a² - b² we get,

→ [ (- 1)² - d² ] = 8/ - 1

→ 1 - d² = - 8

→ 1 + 8 = d²

→ 9 = d²

→ d = 3

Hence,

• a - d = - 1 - 3 = - 4
• a = - 1
• a + d = - 1 + 3 = 2

Now,

Finding Sum of their squares :

→ (a - d)² + a² + (a + d)²

→ ( - 4)² + ( - 1)² + (2)²

→ 16 + 1 + 4

→ 21

Hence, the sum of the squares of the three terms is 21.

Answer 2

Solution :-

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,−4

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