Question
If x2 - 3x + 1 = 0, then the value of $${x^2} + x + \frac{1}{x} + \frac{1}{{{x^2}}}$$ is?
Answer: Option A
$$\eqalign{
& {x^2} - 3x + 1 = 0 \cr
& \Rightarrow {x^2} + 1 = 3x \cr
& \Rightarrow x + \frac{1}{x} = 3 \cr
& {\text{Squaring both sides}} \cr
& \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 9 \cr
& \Rightarrow {x^2} + \frac{1}{{{x^2}}} = 7 \cr
& \therefore {x^2} + x + \frac{1}{x} + \frac{1}{{{x^2}}} \cr
& \Rightarrow {x^2} + \frac{1}{{{x^2}}} + x + \frac{1}{x} \cr
& \Rightarrow 7 + 3 \cr
& \Rightarrow 10 \cr} $$
Was this answer helpful ?
$$\eqalign{
& {x^2} - 3x + 1 = 0 \cr
& \Rightarrow {x^2} + 1 = 3x \cr
& \Rightarrow x + \frac{1}{x} = 3 \cr
& {\text{Squaring both sides}} \cr
& \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 9 \cr
& \Rightarrow {x^2} + \frac{1}{{{x^2}}} = 7 \cr
& \therefore {x^2} + x + \frac{1}{x} + \frac{1}{{{x^2}}} \cr
& \Rightarrow {x^2} + \frac{1}{{{x^2}}} + x + \frac{1}{x} \cr
& \Rightarrow 7 + 3 \cr
& \Rightarrow 10 \cr} $$
Was this answer helpful ?
More Questions on This Topic :
Question 1. If xy + yz + zx = 0, then **Hidden Equation**
Question 6. If x = y + z then x3 - y3 - z3 is?....
Question 7. If **Hidden Equation** is?
Question 8. If **Hidden Equation** ....
Question 10. **Hidden Equation** then x is equal to?....
Latest Videos
Latest Test Papers
Submit Solution