How do you solve $\sqrt{y + 21} - 1 = \sqrt{y + 12}$ $sqrt(y+21)-1=sqrt(y+12)$ ?

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Answer 1 · 2015-10-17T16:14:11

The solution is $y = 4$ $y=4$ .

Square both terms:

$y + 21 - 2 \sqrt{y + 21} + 1 = y + 12$ $y+21 - 2sqrt(y+21) + 1 = y+12$ .

Isolate the root:

$y + 21 - y - 12 + 1 = 2 \sqrt{y + 21}$ $y+21 - y - 12 +1 = 2sqrt(y+21)$ , which simplifies into

$2 \sqrt{y + 21} = 10$ $2sqrt(y+21) = 10$

Square both terms again:

$4 (y + 21) = 100 \Leftrightarrow 4 y + 84 = 100 \Leftrightarrow 4 y = 16$ $4(y+21)=100 \iff 4y+84 = 100 \iff 4y=16$ .

Solving by $y$ $y$ , we get $y = 4$ $y=4$ .

This solution is acceptable, since both the original square roots are well defined in that point.

How do you solve √y+21−1=√y+12sqrt(y+21)-1=sqrt(y+12)?