Question : If $m+n=1$, then the value of $m^{3}+n^{3}+3mn$ is equal to:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
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Correct Answer: 1
Solution : Given: $m+n=1$ Cubing both sides, we get $(m+n)^3=1^3$ ⇒ $m^3+n^3+3mn(m+n)=1$ Putting the value of $(m+n)$ ⇒ $m^3+n^3+3mn(1)=1$ Thus, $m^3+n^3+3mn=1$ Hence, the correct answer is 1.
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Question : If $m-n=2$ and $mn=15,(m,n>0)$ , then the value of $(m^2-n^2)(m^3-n^3)$ is:
Question : If $m x^m-n x^n=0$, then what is the value of $\frac{1}{x^m+x^n}+\frac{1}{x^m-x^n}$ terms of $x^n$ is: Where $x,m,n$ are $>0$
Question : If $m=\sqrt{5+\sqrt{5+\sqrt{5+........}}}$ and $n=\sqrt{5-\sqrt{5-\sqrt{5...........}}}$ then among the following, the relation between m and n is:
Question : If $m+\frac{1}{m-2}=4$, then find the value of $(m-2)^2+\frac{1}{(m-2)^2}$.
Question : If $x+\frac{1}{x}=2$, then the value of $x^{2}+\frac{1}{x^{6}}$ is equal to:
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