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seropon [69]
3 years ago
9

Find two consecutive integers such that the sum of their squares is 145.

Mathematics
1 answer:
DiKsa [7]3 years ago
7 0

Answer: 8 and 9 or -9 and -8

Step-by-step explanation:

Let x be the first of the two integers. Then, since the numbers are consecutive, x+1 is the other integer. We then know that the sum of the squares of x and x+1 is equal to 145. So, now we have the equation

x^2+(x+1)^2=145

which can be expanded and simplified to

2x^2+2x+1=145

which then gives us the quadratic equation

2x^2+2x-144=0

This can then be factored into

2(x^2+x-72)=0

Which can be simplified further into

2(x-8)(x+9)=0

So either x=8 or x=-9. This gives us two solutions: 8 and 9 or -9 and -8.

Hope this helps! CHEERS!

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