the sum of their squares is 53. find both numbers

Question

one negative number is 5 more than another. the sum of their squares is 53. find both numbers

Answer 1

Because a negative number is greater than the other, we can tell that both numbers are negative. because a negative times a negative is a positive, we can find the numbers as a positive and then make them a negative when we give our answer.

 

One number=x

Another number = x+5

So, we can write the equation:

x²+(x+5)²=53 then solve.

x²+ (x+5)(x+5)=53

x²+x²+10x+25=53

2x²+10x+25=53

Make it equal to 0 in order to factor.

2x²+10x-28=0

(2x+ )(x- )

1    28

2    14

 

(2x+14)(x-2)=0

Make them both equal to 0

2x+14=0

2x=-14

x=-7

x-2=0

x=2

 

There are your two answers. -7 and -2.

Check

(-7)²+(-2)²=53

49+4=53

That statement is true, so our numbers are correct.