Two positive numbers have a difference of 8 and a product of 33. What are these numbers?
Solution:
Given, two positive numbers have a difference of 8 and a product of 33.
Le the first number be x
Second number be y
x - y = 8 -------------- (1)
x × y = 33 ------------ (2)
From (2), y = 33 / x
Substitute the value in (1)
x - 33/x = 8
x2 - 33 = 8x
x2 - 8x - 33 = 0
x2 - 11x + 3x - 33 = 0
x(x - 11) + 3(x - 11) = 0
(x + 3)(x - 11) = 0
x = -3 or 11
Since the given number is positive, x = 11
Put the value of x in (1)
11 - y = 8
y = 11 - 8
y = 3
Verification:
1) difference between numbers is 8
x - y = 8
LHS = 11 - 3
= 8
RHS = 8
LHS = RHS
2) product of two number is 33
x × y = 33
LHS = 11 × 3
= 33
RHS = 33
LHS = RHS
Hence proved.
Therefore, the two positive numbers are x = 11 and y = 3.
Two positive numbers have a difference of 8 and a product of 33. What are these numbers?
Summary:
Two positive numbers have a difference of 8 and a product of 33. The numbers are 11 and 3.
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