Answer:
Solution:
Let x the number
1/x its reciprocal
Then,
x - 1/x = 8/3
x(x) - 1/x = 8/3
[tex]x^{2}[/tex] -1/x = 8/3
3([tex]x^{2}[/tex] - 1) = 8x (Multiplication Property of Equality (MPE)
3[tex]x^{2}[/tex] - 3 = 8x
[tex]3x^{2}[/tex] - 8x - 3 = 0
(3x + 1)(x - 3) = 0 (Zero Product Property)
3x + 1 = 0 l x - 3 = 0
3x = -1 l x = 3
3x/3 = -1/3
x = -1/3
Ignore natin yung negative answer then only the positive ang ating gagamitin, therefore the value of x = 3.
Checking:
The original number is 3
The reciprocal is 1/3
Now,
Original - reciprocal of the original
3 - 1/3 = 3(3) -1/3
= 9 - 1/3
= 8/3
Thank you!
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Step-by-step explanation:
