Math, asked by amitshah0512, 1 year ago

8. The sum of three numbers in AP is-3 and their product is 8, then sum of squares of the numbers is
a)9
b)10
c)12
d)21​

Answers

Answered by Anonymous
30

Solution

Option (D) is correct

Given

  • Sum of the three numbers is - 3

  • Product of the three numbers is 8

To finD

Sum of Square of the numbers

Let the three numbers be a - d,a and a + d

Therefore,

 \sf \: a + (a + d) + (a - d) =  - 3 \\  \\  \leadsto \:  \sf \: 3a =  - 3 \\  \\  \leadsto \:  \boxed{ \boxed{ \sf \: a =  - 1}}

Also,

 \sf \: a(a  + d)(a - d) = 8 \\  \\  \leadsto \:  \sf \:  {a}^{3}  -  {ad}^{2}  = 8 \\  \\  \leadsto \:  \sf \: ( - 1) {}^{3}  - ( - 1) {d}^{2}  = 8 \\  \\  \leadsto \:  \sf \: d =  \pm \:  \sqrt{9}  \\  \\  \leadsto \:  \boxed{ \boxed{ \sf d =  \pm \: 3}}

The first term and common difference of the AP are - 1 and ± 3 respectively

Now,

 \sf \:  {a}^{2}  + (a + d) {}^{2}  + (a - d) {}^{2}

Using + 3 or - 3,we would obtain the same result

Thus,

 \implies \:  \sf \: ( - 1) {}^{2}  + ( - 1 +3 \:  ) {}^{2}  + ( - 1  - 3) {}^{2}  \\  \\  \implies \:  \sf \: 1 +  {( 2)}^{2}  +  {( - 4)}^{2}  \\  \\  \implies \:  \sf \: 1 + 4 + 16  \\  \\  \implies  \sf \:  21

Sum of the square of the three numbers is 21

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