Quang H. answered • 09/21/14

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Math and Science Tutor

Given the parameters of the problem, where a number is one more than its reciprocal, we can come up with this equation:

x = (1/x) + 1

We can then multiply both sides of the equation by x and continue on like this:

x

^{2}= (x/x) + xx

^{2 }= 1 + xx

^{2}- x - 1 = 0Now we have a quadractic equation, and we can plug in the values into the quadratic formula:

x = -b ± √(b

^{2}- 4ac) 2a

x = (1) ± √((1) - 4 (1)(-1)

2(1)

x = 1.618, -.618

If we add the numbers in the second sentence of your problem together like this:

x

^{4}+ (1/x)^{4}where x can be either of the two numbers we found from the quadratic formula, the answer will be 7.