Question

The sum of a number and its reciprocal is 8. find this number

Answer 1

You have said that x + 1/x = 8

Multiply each side by 'x' : x² + 1 = 8x

Subtract 8x from each side: x² - 8x + 1 = 0

Solving this quadratic equation by means of the quadratic formula,
(the procedure is left as an exercise for the student), the two
solutions are:

x = 4 + √15 = 7.873 (rounded)
and
x = 4 - √15 = 0.127 (rounded)

Answer 2

`x+(1)/(x)=8\\\\(x^2)/(x)+(1)/(x)=8\\\\(x^2+1)/(x)=8\\\\x^2+1=8x\\\\x^2-8x+1=0`


`a=1;\ b=-8;\ c=1\\\\\Delta=b^2-4ac\to\Delta=(-8)^2-4\cdot1\cdot1=64-4=60\\\\x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(60)=√(4\cdot15)=2√(15)\\\\x_1=(8-2√(15))/(2\cdot1)=4-√(15);\ x_2=(8+2√(15))/(2\cdot1)=4+√(15)\\\\Answer:4-√(15)\ or\ 4+√(15).`