# How do you solve sqrt(a+21)-1=sqrt(a+12)?

the answer is $a = 4$

#### Explanation:

the given equation is $\sqrt{a + 21} - 1 = \sqrt{a + 12}$
squaring on both sides we get
$a + 21 + 1 - 2 \sqrt{a + 21} = a + 12$
simplifying we get $2 \sqrt{a + 21} = 10 \Rightarrow \sqrt{a + 21} = 5$
squaring on both sides we get
$a + 21 = 25 \Rightarrow a = 4$

Nov 8, 2017

$a = 4$

#### Explanation:

$\sqrt{a + 21} - 1 = \sqrt{a + 12}$

$\sqrt{a + 21} - \sqrt{a + 12} = 1$

After using difference of squares identity,

$\frac{\left(a + 21\right) - \left(a + 12\right)}{\sqrt{a + 21} - \sqrt{a + 12}} = \frac{9}{1}$

$\sqrt{a + 21} + \sqrt{a + 12} = 9$

Hence,

$\sqrt{a + 21} + \sqrt{a + 12} + \sqrt{a + 21} - \sqrt{a + 12} = 9 + 1$

$2 \sqrt{a + 21} = 10$

$\sqrt{a + 21} = 5$

$a + 21 = 25$

$a = 4$