Question

Q1.IF X²+1/X²=18, THEN THE VALUE OF X+1/X WILL BE?

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Answer 1

Step-by-step explanation:

Answer:

$\begin{gathered}\text{Given: } x^2 + \dfrac{1}{x^2} = 18\\\\\\\text{To Find: } x + \dfrac{1}{x} = ?\\\\\\\text{Squaring the "To Find" part we get:}\\\\\\\implies (x + \dfrac{1}{x})^2 = x^2 + \dfrac{1}{x^2} + 2\times x\times \dfrac{1}{x}\\\\\\\implies (x + \dfrac{1}{x})^2 = 18 + 2 ( 1 )\\\\\\\implies (x + \dfrac{1}{x})^2 = 20\end{gathered}$

Taking square root on both sides we get:

$\begin{gathered}\implies (x + \dfrac{1}{x} ) = \sqrt{20} \\\\\implies \boxed{ \bf{(x + \dfrac{1}{x} ) = 2 \sqrt{5}}}\end{gathered}$

Hence the required answer is 2√5.

Answer 2

Given Equation is x^2 + 1/x^2 = 18

= > x^2 + (1/x^2) = 2 + 16

= > x^2 + (1/x^2) - 2 = 16

We can write it as,

= > x^2 + (1/x^2) - 2 * x * (1/x) = 16

We know that a^2 + b^2 - 2ab = (a - b)^2

= > (x - 1/x)^2 = 16

= > Answer : \boxed { x - \frac{1}{x} = +4, -4 }}