# Two integers have a difference of 4. The sum of their squares is 250. Determine the integers.?

### 12 Answers

- PinkgreenLv 71 month ago
Let the integers be x, y & x>y then

x-y=4

x^2+y^2=250

=>

(y+4)^2+y^2=250

=>

2y^2+8y+16=250

=>

y^2+4y-117=0

=>

(y+13)(y-9)=0

=>

y=-13 or y=9

and

x=-9 or x=13

correspondingly.

=>

answers:

x=-9 & y=-13

or

x=13 & y=9

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- lenpol7Lv 71 month ago
Let the integers be 'm' & 'n'

m - n = 4

m^2 + n^2 = 250

Hence

m = 4 + n

Substitute

(4 + n)^2 + n^2 = 250

16 + 8n + n^2 + n^2 = 250

2n^2 + 8n - 234 = 0

2(n^2 + 4n - 117) = 0

Factor

(n - 9)(n + 13) = 0

Hence n = 9 & m = 13

- DixonLv 71 month ago
Seeing as 4 << 250, the integers are similar and they will be approx

√(250/2) ± 2

= 11.1 ± 2

= 9 , 13

Check

9² + 13² = 81 + 169 = 250

- Engr. RonaldLv 71 month ago
ley x and y are integers

x - y = 4 eq1

x^2 + y^2 = 250 eq2

from eq1 let x your subject.

x - y = 4

x = y + 4

plug in eq1 to eq2

x^2 + y^2 = 250

(y + 4)^2 + y^2 = 250

y^2 + 8y + 16 + y^2 = 250

2y^2 + 8y + 16 - 250 = 0

2y^2 + 8y - 234 = 0

y^2 + 4y -117 = 0

(y + 13)(y - 9) = 0

y + 13 = 0, y - 9 = 0

y = - 13, y = 9

solving for x from eq1

when y = - 13

x = - 13 + 4 = -9

when y = 9

x = 9 + 4 = 13

The integers are: -13, 9, -9, 13..

- KrishnamurthyLv 71 month ago
Two integers have a difference of 4.

The sum of their squares is 250.

Determine the integers.

x - y = 4

x^2 + y^2 = 250

2y^2 + 8y - 234 = 0

2(y^2 + 4y - 117) = 0

y = 9

The two integers are 13 and 9.

- jacob sLv 71 month ago
x-y=4

x^2 + y^2=250

y=4+x

x^2 +(4+ x)^2 =250

x^2 + x^(2)+8*x+16= 250

2x^2 + 8x - 234=0

2*(x-9)*(x+13)=0

x=9 , x= -13

substitute in y=4 +x

y= 4 + 9

y=13

13-9=4 checked

13^2 + 9^2=250

169 +81=250 checked

x=9 , y= 13 your two integers

- 1 month ago
a - b = 4

a^2 + b^2 = 250

(a - b)^2 = 4^2

a^2 - 2ab + b^2 = 16

250 - 2ab = 16

125 - ab = 8

117 = ab

a = 4 + b

117 = b * (b + 4)

117 = b^2 + 4b

117 + 4 = b^2 + 4b + 4

121 = (b + 2)^2

-11 , 11 = b + 2

-13 , 9 = b

a = 4 + b

a = -9 , 13

-13 , -9

and

9 , 13