Question

Sum of square of a number and square of its reciprocal is 17/4,
a, Find the sum of the number and its reciprocal?
b, What is the number?
Please help me fast....​

Answer 1

Answer:

$x = 2 \: and \: \: x = \frac{1}{2}$

Step-by-step explanation:

Let the number be x

Given

${x}^{2} + \frac{1}{ {x}^{2} } = \frac{17}{4}$

Consider the following

$(x + \frac{1}{x} )^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x}$

$(x + \frac{1}{x} )^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

$(x + \frac{1}{x} )^{2} = \frac{17}{4} + 2 = \frac{25}{4}$

$(x + \frac{1}{x} ) = ±\frac{5}{2}$

Solving for the positive Value, we have

$2 {x}^{2} - 5x + 2 = 0$

$2 {x}^{2} - 4x - x + 2 = 0$

$(2x - 1)(x - 2) = 0$

$2x(x - 2) - 1(x - 2) = 0$

$x = 2 \: \: \: \: and \: x = \frac{1}{2}$

Similarly we can solve for the negative Value also and we get

x=-2 and (-1/2)