Answer:
(0.0147, 4.0147) and (-4.04, 0.04)
Step-by-step explanation:
Let the smaller number be x
Let the larger number be y
If a positive integer is 4 less than another, then;
x = y - 4 ...1
If 3 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer and result is -67, then;
1/y - 3(1/x) = -67
1/y -3/x = -67 ...2
Substitute 1 into 2
1/y - 3/y-4 = -67
y-4-3y/y(y-4) = -67
-4-2y = -67(y^2-4y)
- 4-2y = -67y^2 +268y
-67y^2 +268y+2y + 4 = 0
-67y^2 +270y + 4 =0
67y^2 -270y - 4 = 0
Factorize
-270±√270² - 4(-4)(67)/2(67)
= -270±√72,900+1072/134
= -270±271.97/134
= -270 -271.97/134 and -270 +271.97/134
= -541.97/134 and 1.97/134
x = 0.0147 and -4.04
y = x+4
y = 0.0147+4
y = 4.0147
If x = -4.04
y = -4.04 + 4
y = 0.04
Hence the pair of values are (0.0147, 4.0147) and (-4.04, 0.04)
