Find the consecutive integers whose square have the sum 340.
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The consecutive positive integers will be 12 and 14 (even positive not odd).
Explanation :
Let one number be x and other be x+2 (because it will be positive even integers so x+2). Squaring and adding both,
Now write out the equation according to the question
(x)^2+(x+2)^2=340
x^2+x^2+4x+4=340
Combining like terms,
2x2+4x+4=340
2x^2+4x−336=0
(2x+28)(x−12)=0
x=−14,12
x=12 because the answer must be positive according to the question.
So x+2 =14.
You can also manually check,
12^2 + 14^2 = 144+196
=340
Explanation :
Let one number be x and other be x+2 (because it will be positive even integers so x+2). Squaring and adding both,
Now write out the equation according to the question
(x)^2+(x+2)^2=340
x^2+x^2+4x+4=340
Combining like terms,
2x2+4x+4=340
2x^2+4x−336=0
(2x+28)(x−12)=0
x=−14,12
x=12 because the answer must be positive according to the question.
So x+2 =14.
You can also manually check,
12^2 + 14^2 = 144+196
=340
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