Question

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

Answer 1

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+1-2sqrt(a+21)=a+12`
simplifying we get `2sqrt(a+21)=10rArrsqrt(a+21)=5`
squaring on both sides we get
`a+21=25rArra=4`

Answer 2

`a=4`

Explanation:

`sqrt(a+21)-1=sqrt(a+12)`

`sqrt(a+21)-sqrt(a+12)=1`

After using difference of squares identity,

`[(a+21)-(a+12)]/[sqrt(a+21)-sqrt(a+12)]=9/1`

`sqrt(a+21)+sqrt(a+12)=9`

Hence,

`sqrt(a+21)+sqrt(a+12)+sqrt(a+21)-sqrt(a+12)=9+1`

`2sqrt(a+21)=10`

`sqrt(a+21)=5`

`a+21=25`

`a=4`