Question : If $a^3b=abc=180;\ a, b$, and $c$ are positive integers, then the value of $c$ is:
Option 1: 110
Option 2: 1
Option 3: 4
Option 4: 25
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Correct Answer: 1
Solution : Given: $a^3b=abc=180;\ a, b$ and $c$ are positive integers. The factors of $180 = 2 × 2 × 3 × 3 × 5$ Since $a^3b$ contains the cube of $a$. So, $a =1$ is the only possibility. Also $a^3b=abc$ ⇒ $a^2=c$ So, $c=1$ Hence, the correct answer is $1$.
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Question : If $a+b+c=15$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{71}{abc}$, then the value of $a^{3}+b^{3}+c^{3}-3abc$ is:
Question : If $a+b+c=5, a^3+b^3+c^3=85$, and $abc=25$, then find the value of $a^2+b^2+c^2-a b- bc - ca$.
Question : If $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, then the value of $\frac{ab+bc+ca}{abc}$ is:
Question : If $a, b, c$ are real numbers and $a^{2}+b^{2}+c^{2}=2(a-b-c)-3,$ then the value of $a+b+c$ is:
Question : If $\frac{A}{3}=\frac{B}{2}=\frac{C}{5}$, what is the value of ratio $(C+A)^{2}:(A+B)^{2}:(B+C)^{2}$?
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