Question

If sum of the three numbers in A.P. is 78 and their product is 15470, then sum of squares of the three numbers is​

Answer 1

Answer:

2190

Step-by-step explanation:

Let the numbers be a-b, a, a+b are in A.P

Sum is 78, a-b+a+a+b=78

3a=78

a=78/3

a=26

Product is 15470, (a-b)(a)(a+b)=15470

(a^2-b^2)a=15470

a^3-ab^2=15470

(26)^3-26b^2=15470

17,576-15740=26b^2

2106=26b^2

2106/26=b^2

81=b^2

b=√81

b=9

The numbers are (26-9), 26, (26+9) = 17, 26, 35

Sum of squares of numbers is 17^2+26^2+35^2

= 289+676+1225

=2190

Answer 2

Answer:

The sum of squares of the three numbers is​ 2190.

Step-by-step explanation:

As per the data given in the question

We have to calculate sum of squares of the three numbers.

As per the question

It is given that

sum of the three numbers in A.P. is 78 and their product is 15470

Let the three numbers in A.P. be a-d, a, a+d

According to given information

Sum= a-d+a+a+d = 78

⇒3a = 78

⇒a= 26

and product is = (a-d)*a*(a+d)

⇒$a^{2}-ad$ (a+d)

⇒$a^{3}+a^{2}d-a^{2}d-ad^{2}$

⇒$a^{3}-ad^{2}$ = 15470

put the value of a=26

then we get

= 17576-26$d^{2}$ =15470

= 26$d^{2}$ = 2106

= d=$\sqrt{81}=9$

so, a=26 and d=9

Therefore when d=9 and a=26 then a-d = 26-9=17

when d=9 and a=26 then a+d = 26+9=35

and a=26

then three numbers are 17,26,35

According to questions

sum of squares of the three numbers is​

$17^{2}+26^{2}+35^{2}$

= 289+676+1225

=2190

Hence, the sum of squares of the three numbers is​ 2190.

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