If $2 (a^{2} - b^{2}) = 44$ $2(a^2-b^2) = 44$ and $a - b = 2$ $a-b=2$ , what is the value of $a + b$ $a+b$ ?

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If $2 (a^{2} - b^{2}) = 44$ $2(a^2-b^2) = 44$ and $a - b = 2$ $a-b=2$ , what is the value of $a + b$ $a+b$ ?

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Answer 1 · 2017-11-01T16:07:03

$11$ $11$

Explanation:

$2 (a^{2} - b^{2}) = 44 - - (1)$ $2(a^2-b^2)=44--(1)$

and

$a - b = 2 - - - (2)$ $a-b=2---(2)$

from

$(1) \to (a^{2} - b^{2}) = \frac{44}{2} = 22$ $(1)rarr(a^2-b^2)=44/2=22$

using difference of squares

$(a - b) (a + b) = 22$ $(a-b)(a+b)=22$

from

$(2) \to 2 (a + b) = 22$ $(2)rarr2(a+b)=22$

$\Rightarrow a + b = 11$ $=>a+b=11$

Answer 2 · 2017-11-01T16:11:50

11

Explanation:

$a - b = 2$ $a-b=2$
$a = 2 + b$ $a=2+b$

$2 (a^{2} - b^{2}) = 44$ $2(a^2-b^2)=44$
$2 ({(2 + b)}^{2} - b^{2}) = 44$ $2((2+b)^2-b^2)=44$
${(2 + b)}^{2} - b^{2} = 22$ $(2+b)^2-b^2=22$
$b^{2} + 4 b + 4 - b^{2} = 22$ $b^2+4b+4-b^2=22$
$4 b + 4 = 22$ $4b+4=22$
$4 b = 18$ $4b=18$
$b = \frac{9}{2}$ $b=9/2$

$a - b = a - \frac{9}{2} = 2$ $a-b=a-9/2=2$
$a = \frac{13}{2}$ $a=13/2$

$a = \frac{13}{2}$ $a=13/2$ , $b = \frac{9}{2}$ $b=9/2$

$a + b = \frac{13}{2} + \frac{9}{2} = 11$ $a+b=13/2+9/2=11$

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If $2 (a^{2} - b^{2}) = 44$ $2(a^2-b^2) = 44$ and $a - b = 2$ $a-b=2$ , what is the value of $a + b$ $a+b$ ?

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Explanation:

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If 2(a2−b2)=442(a^2-b^2) = 44 and a−b=2a-b=2, what is the value of a+ba+b?

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Explanation:

Explanation:

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If $2 (a^{2} - b^{2}) = 44$ $2(a^2-b^2) = 44$ and $a - b = 2$ $a-b=2$ , what is the value of $a + b$ $a+b$ ?