Question

The sum of the three consecutive integers is 30.
Find the sum of their squares.​

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Answer 1

As per the data given in the question,

We have to determine the sum of square of three consecutive integers.

As per question,

it is given that,

Sum of three consecutive integers = 30.

So, let the three consecutive integers are $x, (x+1), (x+2)$

So, from above,

We can write it as,

$x+(x+1)+(x+2)=30\\=>3x+3 = 30\\=>3x = 27\\=>x = \frac{27}{3} = 9$

So, the value of integers will be 9, 10, 11.

So, there sum will be $=9^2+10^2+11^2 = 81+100+121 = 302$

Answer 2

Given: The sum of the three consecutive integers is 30.

We have to find the sum of their squares.​

We are solving in the following way:

Let assume the three consecutive integers be$x,x+1,x+2$.

From the given statement, we can write:

$\Rightarrow x+x+1+x+2=30\\\Rightarrow 3x+3=30\\\Rightarrow 3x=30-3\\\Rightarrow 3x=27\\\\\Rightarrow x=\frac{27}{3} \\\\\Rightarrow x=9$

So, the three consecutive numbers will be:

$\Rightarrow x=9\\\Rightarrow x+1\Rightarrow 9+1=10\\\Rightarrow x+2\Rightarrow 9+2=11$

The sum of their squares will be:

$\Rightarrow 9^{2} +10^{2} +11^{2} \\\Rightarrow 81+100+121\\\Rightarrow 302$

Hence, the sum of their squares will be$302$.