How smart are you? Can you answer this question?

Question

The difference of two positive numbers is four. The sum of their squares is 170. What are the numbers? Explain.

Lets see who can answer that one!

Answer 1

make the numbers x & y.

x-y = 4
x^2 + y^2 = 170
now solve this equation knowing that
x = 4+y
we get:
(4+y)^2 + y^2 = 170

16 + 8y + 2y^2 = 170
y^2 + 4y - 77 = 0
(y+11)(y-7) = 0

y can be 7 or -11 in which case x= 11 or -7

but only the first case holds to satisfy the requirement that both numbers be positive.

Answer 2

Two equations:

x - y = 4

x^2 + y^2 = 170

so, x = y+4

substitute y +4 into the second equation for x and get:

(y + 4)^2 + y^2 = 170

y^2 + 8y + 16 + y^2 = 170

2y^2 + 8y + 16 = 170

divide by 2

y^2 + 4y + 8 = 85

subtract 85

y^2 + 4y - 77 = 0

factor

(y - 7)(y + 11) = 0

so. y = 7 or -11

no negative numbers per the question's parameters, so

y = 7

x - 7 = 4

so the answer is : 7 and 11

check the answer

7^2 + 11^2 = 170

49 + 121 = 170

170 = 170.

Answer 3

A little algebra will suffice. Let the numbers be x and y. We are given x = y-4; x^2 + y^2 = 170. Then, (y-4)^2 + y^2 = 170; 2y^2 -8y + 16 = 170; y^2 -4y -77 = 0; and the numbers are 7 and 11.

Answer 4

let x and y be the two numbers
x - y = 4
x^2 + y^2 = 170

x = y + 4

(y + 4)^2 + y^2 = 170
y^2 + 8y + 16 + y^2 = 170
2y^2 + 8y - 154 = 0
2 (y + 4y - 77) = 0
2 (y + 11) (y - 7) = 0
y = -11 or 7

since the question ask for a positive number, take 7

x - y = 4
x - 7 = 4
x = 11

so 11 and 7

Answer 5

x-y =4

x^2 + y^2 = 170

Substituting (4+y) for x in the second equation yields

y^2 + 4 y - 77 =0

which has a positive root at 7.

y=7
x=11

and indeed, 49+121 = 170

Answer 6

To answer your first question: not very smart.

Second question:
x - y = 4
x^2 + y^2 = 170

x - y = 4
Add y to both sides:
x = 4 + y

Substitute x=4+y:
(4 + y)^2 + y^2 = 170
F.o.i.l. out first term:
16 + 8y + y^2 + y^2 = 170
Subtract 170 from both sides:
-154 +8y + 2y^2 = 0
Rearrange terms and divide both sides by 2:
y^2 + 4y - 77 = 0
Factor:
(y + 11)(y - 7) = 0
y = -11 (this is negative so it doesn't work)
or
y = 7

So y = 7

x - 7 = 4
x = 11

The two numbers are 7 and 11.

Answer 7

ok this could be answered in many forms...

let the number be x and the other be x + 4... difference can be seen in any form you want to see... the difference between x+4 and x is 4...

x^2 + (x+4) ^ 2 = 170... rest is simple algebra...

Answer 8

What you said was :

x² + (x + 4)² = 170.

So 2x² + 8x - 154 = 0.

Or 1x² + 4x - 77 = 0

Factor or use the quadratic formula.

Go from there.

Answer 9

7 and 11

Answer 10

3 and 7