Question

a^2+2ab+b^2=25, find a+b

Answer 1

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Answer 2

$\displaystyle \bf (a + b) = \pm \: 5$

Given :

$\displaystyle \sf {a}^{2} + 2ab + {b}^{2} = 25$

To find :

The value of a + b

Formula Used :

$\displaystyle \sf {a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2}$

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf {a}^{2} + 2ab + {b}^{2} = 25$

Step 2 of 2 :

Find the value of a + b

$\displaystyle \sf {a}^{2} + 2ab + {b}^{2} = 25$

$\displaystyle \sf{ \implies } {(a + b)}^{2} = 25\: \: \: \bigg[ \: \because \:{a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2} \bigg]$

$\displaystyle \sf{ \implies }a + b = \pm \: \sqrt{25}$

$\displaystyle \sf{ \implies }a + b = \pm \: 5$

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