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Recent questions tagged algebra

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1
GATE2016-GA-9
The binary operation $\square$ is defined as $a \square b = ab+(a+b)$, where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that $a \square x = a$, for any $a$, is $0$ $1$ $2$ $10$
The binary operation $\square$ is defined as $a \square b = ab+(a+b)$, where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, de...
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2
GATE2015-4
Operators $\square$, $\lozenge$ and $\rightarrow$ are defined by: $a \: \square \: b = \dfrac{a-b}{a+b}$; $a \: \lozenge \: b = \dfrac{a+b}{a-b}$; $a \rightarrow b = ab$. Find the value of $(66 \: \square \: 6) \rightarrow (66 \: \lozenge \: 6)$. $-2$ $-1$ $1$ $2$
Operators $\square$, $\lozenge$ and $\rightarrow$ are defined by: $a \: \square \: b = \dfrac{a-b}{a+b}$; $a \: \lozenge \: b = \dfrac{a+b}{a-b}$; $a \rightarrow b = ab$....
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3
GATE2018-GA-9
If $x^2 + x – 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$? $1$ $5$ $7$ $9$
If $x^2 + x – 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$?$1$$5$$7$$9$
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