Question : If $\frac{a}{b}+\frac{b}{a}=1$, then the value of $(a^3+b^3)$ is:
Option 1: 1
Option 2: 0
Option 3: –1
Option 4: 2
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Correct Answer: 0
Solution : Given: $\frac{a}{b}+\frac{b}{a}=1$ ⇒ $\frac{a^2+b^2}{ab}=1$ ⇒ $a^2+b^2=ab$ Now, $(a^3+b^3)=(a+b)(a^2+b^2-ab)$ Substitute the value of $a^2+b^2=ab$ in the above equation, we get, $(a^3+b^3)=(a+b)(ab-ab)$ ⇒ $(a^3+b^3)=(a+b)\times0$ ⇒ $(a^3+b^3)=0$ Hence, the correct answer is 0.
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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 $(a\neq 0)$:
Question : If $\frac{a}{b}+\frac{b}{a}=-1$ and $a-b=2$, then the value of $a^3-b^3$ is:
Question : If $a+\frac{1}{a-2}=4$, then the value of $(a-2)^{2}+(\frac{1}{a-2})^{2}$ is:
Question : If $a+b=2c$, then the value of $\frac{a}{a–c}+\frac{c}{b–c}$ is equal to (where $a\neq b\neq c$):
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