Answer:
Step-by-step explanation:
Let the number be x.
The reciprocal of the number will be 1/x
If the sum of the number and its reciprocal is 41/20, this can be represented as;
[tex]x+\frac{1}{x} = 41/20\\\frac{x^{2}+1}{x} = \frac{41}{20} \\20x^{2} +20 = 41x\\20x^{2} -41x+20 = 0\\[/tex]
Uisng the general formula to get x
x = -b±√b²+4ac/2a
x = 41±√41²-4(20)(20)/2(20)
x = 41±√1681-1600/40
x = 41±√81/40
x = 41±9/40
x = 50/40 or 32/40
x = 5/4 or 4/5
if the value is 5/4, the other value will be 4/5
The numbers are 5/4 and 4/5
The smaller value is 4/5
The larger value is 5/4
Answer:
a=5/4 or 4/5
Therefore, the smaller value = 4/5
The larger value = 5/4
Step-by-step explanation:
Let the number be represented by a
And it's reciprocal be represented by 1/a
So we have
a + 1/a = 41/20
Cross Multiply
20( a +1/a) = 41
20a +20/a =41
Find the LCM which is a
20a² + 20 = 41a
20a² + 20 - 41a =0
20a² - 41a +20 = 0
20a²-25a - 16a + 20 =0
5a(4a - 5) -4( 4a - 5) = 0
(5a - 4)(4a - 5) = 0
5a - 4 = 0
5a = 4
a = 4/5
or
4a - 5 = 0
4a =5
a = 5/4
Therefore, the number which is represented by a is
1) a = 4/5 while it's reciprocal which is 1/a is 5/4
or
2) a = 5/4 which it's reciprocal which is 1/a = 4/5
Therefore, the smaller value = 4/5
The larger value = 5/4
