Question

The sum of the square of three consecutive odd numbers is 2195. Find the numbers​

Answer 1

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Answer 2

ANSWER:  

The sum of the square of three consecutive odd numbers is 2195. The numbers are 25, 27 and 29

SOLUTION:

Given, the sum of the square of three consecutive odd numbers is 2195.  

We have to find the numbers.

Let the small number be x, then remaining two numbers is x + 2, x + 4.

Then according to given information,

$\begin{array}{l}{x^{2}+(x+2)^{2}+(x+4)^{2}=2195} \\\\ {x^{2}+\left(x^{2}+4+4 x\right)+\left(x^{2}+16+8 x\right)=2195} \\\\ {3 x^{2}+12 x+20=2195} \\\\ {3 x^{2}+12 x+20-2195=0}\end{array}$

$\begin{array}{l}{3 x^{2}+12 x-2175=0} \\\\ {3\left(x^{2}+4 x-725\right)=0} \\\\ {x^{2}+4 x-725=0}\end{array}$

$\begin{array}{l}{x^{2}+4 x-29 \times 25=0} \\\\ {x^{2}+(29-25) x-29 \times 25=0} \\\\ {x^{2}+29 x-25 x-29 \times 25=0}\end{array}$

x(x + 29) – 25(x + 29) = 0

(x + 29)(x – 25) = 0

x = 25 or -29 [we can neglect negative numbers.]

So, the three consecutive numbers are 25, 25 + 2, 25 + 4

Hence, the three numbers are 25, 27, 29.