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Explanation
- The difference between two integers is 5.
- Their product is 500.
- The number will be figure out in this way.
Let suppose the integers are y and z.
The difference between two integers is 5
y – z = 5 ________ (i)
The product of the integers is 500
yz = 500 ________ (ii)
By solving equation (i) and (ii) simultaneously, we can easily find out the value of y (y = 25) and z (z = 20).
To Find
Numbers = ?
Solution
Let suppose
Integers are y and z.
According to the given conditions
y – z = 5 ________ (i)
yz = 500
y = 500/z ________ (ii)
Putting y = 500/z in equation (i)
500/z – z = 5
500 – z2 = 5z
z2 + 5z – 500 = 0
z2 + 25z – 20z – 500 = 0
z(z + 25) – 20(z + 25) = 0
(z + 25)(z – 20) = 0
z + 25 = 0 & z – 20 = 0
z = -25 (not possible) & z = 20 (possible)
Put z = 20 in equation (i)
y – 20 = 5
y = 5 + 20
y = 25
Required Numbers = 20 & 25 answer
Conclusion
The difference between two integers is 5. Their product is 500. The numbers are 20 and 25.
