Question : If the sum of a number and its reciprocal is 2. Then the number is:
Option 1: 0
Option 2: 1
Option 3: –1
Option 4: 2
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Correct Answer: 1
Solution : Given: Sum of a number and its reciprocal is 2 Let the first and second numbers be $x$ and $\frac{1}{x}$. $x+\frac{1}{x} =2$ ⇒ $(x+\frac{1}{x}) ^{2}=2^{2}$ ⇒ $x^{2}+\frac{1}{x^{2}}+2= 4$ ⇒ $x^{2}+\frac{1}{x^{2}} = 2$ ⇒ $x^{2}+\frac{1}{x^{2}} –2=0$ ⇒ $(x-\frac{1}{x}) ^{2}=0$ ⇒ $x^{2}=1$ $\therefore x=1$ Hence, the correct answer is 1.
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Question : If the sum of the roots of a quadratic equation is 1 and the product of the roots is –20, find the quadratic equation.
Question : The sum of a non-zero number and twice its reciprocal is $\frac{33}{4}$. Find the number.
Question : A number is greater than 58 times its reciprocal by $\frac{3}{4}$. What is the number?
Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:
Question : If $a+\frac{1}{a}=1$, then the value of $\frac{a^2-a+1}{a^2+a+1}$ is $(a\neq 0)$:
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