a^2 −b^2 =15 2a−b=?


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Question Number 122405 by Khalmohmmad last updated on 16/Nov/20

$a^{2} - b^{2} = 15$ $2 a - b = ?$
Commented by Dwaipayan Shikari last updated on 16/Nov/20

$I n f i n t e l y m a n y a n s w e r s$ $a = \sqrt{15}, b = 0$ $2 a - b = 2 \sqrt{15}$ $a = 4 b = 1$ $2 a - b = 7$ $. . . .$
	Answered by ajfour last updated on 16/Nov/20

	$a = \pm \sqrt{b^{2} + 15}$ $2 a - b = - b \pm 2 \sqrt{b^{2} + 15}$ $A s o n e e x a m p l e f o r i n t e g r a l s o l u t i o n$ $l e t b = 1$ $2 a - b = - 1 \pm 8 = 7, - 9$
	Answered by mr W last updated on 16/Nov/20

	$(a - b) (a + b) = 15 = 1 \times 15 = 3 \times 5$ ${\begin{cases} a - b = 1 \\ a + b = 15 \end{cases} \Rightarrow a = 8, b = 7 \Rightarrow 2 a - b = 9$ ${\begin{cases} a - b = - 1 \\ a + b = - 15 \end{cases} \Rightarrow . . .$ ${\begin{cases} a - b = 15 \\ a + b = 1 \end{cases} \Rightarrow . . .$ ${\begin{cases} a - b = - 15 \\ a + b = - 1 \end{cases} \Rightarrow . . .$ ${\begin{cases} a - b = 3 \\ a + b = 5 \end{cases} \Rightarrow a = 4, b = 1 \Rightarrow 2 a - b = 7$ $. . . . . .$
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