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Home Question Bank Math Algebra Archive 2025 January 04

Algebra Questions from Jan 04,2025

Browse the Algebra Q&A Archive for Jan 04,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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11. Combine like terms. \( (-3 y-5)+(5 m+7 y)+(6+9 m) \) \( \left. \begin{array} { l } { x + \frac { 1 } { y } ) ^ { - 2 } + ( \frac { 1 } { y } + x ) ^ { - 2 } = \frac { 149 } { 1225 } } \\ { ( x - \frac { 1 } { y } ) ^ { - 2 } + ( \frac { 1 } { y } - x ) ^ { - 2 } = \frac { 29 } { 25 } } \end{array} \right. \) \( \left. \begin{array} { l } { x + \frac { 1 } { y } ) ^ { - 2 } + ( \frac { 1 } { y } + x ) ^ { - 2 } = \frac { 149 } { 1225 } } \\ { ( x - \frac { 1 } { y } ) ^ { - 2 } + ( \frac { 1 } { y } - x ) ^ { - 2 } = \frac { 29 } { 25 } } \end{array} \right. \) 10. Find the sum. \( (8 b+7)+(6 x-4)+(5 c+8) \) \( \left. \begin{array} { l } { x + \frac { 1 } { y } ) ^ { - 2 } + ( \frac { 1 } { y } + x ) ^ { - 2 } = \frac { 149 } { 1225 } } \\ { ( x - \frac { 1 } { y } ) ^ { - 2 } + ( \frac { 1 } { y } - x ) ^ { - 2 } = \frac { 29 } { 25 } } \end{array} \right. \) \( \left. \begin{array} { c } { a ^ { 2 } \sqrt { a } + b ^ { 2 } \sqrt { b } = 33 } \\ { \sqrt { a } + \sqrt { b } = 3 } \\ { a = ? , b = ? } \end{array} \right. \) What is the value of \( a^0 \) when \( a \neq 0 \)? 1.3 Simplify: \[ \frac{2^{x}-2^{-x}}{4^{x}-1} \] 5. If \( (-9,4) \) is on the graph of \( f \), which of the following ardered pairs is on the graph of \( f^{-1} \) ? A) \( (9,-4) \) B) \( \left(-9, \frac{1}{4}\right) \) C) \( (4,-9) \) D) \( \left(4,-\frac{1}{9}\right) \) Problème \( 1: \) Soient \( x, y \) et \( z \) des nombres reels tels que xy \( =2 \). Prouver que parmi les trois nombres \( 2 x-\frac{1}{y}, 2 y-\frac{1}{z} \) et \( 2 z-\frac{1}{x} \), au plus deux d'entre eux sont strictement supérieurs a 2 .
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