SOLUTION: The difference of two positive integers is 7. Find the 2 positive integers if their product is 42.

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Question 919667: The difference of two positive integers is 7. Find the 2 positive integers if their product is 42.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let two positive integers be x and y
if the difference of two positive integers is 7, then we have:
x-y=7 .......eq.1
if their product is 42,then we have:
x%2Ay=42 .......eq.2

solve the system:
x-y=7 .......eq.1
x%2Ay=42 .......eq.2
________________________________
x%2Ay=42 .......eq.2.......solve for x
x=42%2Fy ........plug it in eq.1

x-y=7 .......eq.1
42%2Fy-y=7 ....solve for y

42%2Fy=y%2B7
42=%28y%2B7%29y
42=y%5E2%2B7y
0=y%5E2%2B7y-42 ....use quadratic formula to solve for y

y=+%28-7+%2B-+sqrt%28+7%5E2-4%2A1%2A%28-42%29+%29%29%2F%282%2A1%29+
y=+%28-7+%2B-+sqrt%28+49%2B168+%29%29%2F2+

y=+%28-7+%2B-+sqrt%28+217+%29%29%2F2+
y=+%28-7+%2B-+14.73091986265624%29%2F2+

solutions:

y=+%28-7+%2B+14.73091986265624%29%2F2+
y=+7.73091986265624%2F2+
y=+3.865459931328118+
y=+3.87+
or
y=+%28-7+-+14.73091986265624%29%2F2+
y=+-21.73091986265624%2F2+
y=+-10.86545993132812+
y=+-10.87+

find x

x=42%2Fy
x=42%2F3.865459931328118
x=10.86545993132812
x=10.87
or
x=42%2Fy
x=42%2F-10.86545993132812+
x=-3.865459931328117
x=-3.87

solution pairs:
x=10.87,y=+3.87+
and
x=-3.87,y=+-10.87+

check eq.1:

x-y=7 .......eq.1 for x=10.87,y=+3.87+
10.87-3.87=7
7=7
x-y=7......eq.1 for x=-3.87,y=+-10.87+
-3.87-%28-10.87%29=7
-3.87%2B10.87=7
7=7