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

2 Answers
Manasvini Nittala
Nov 8, 2017

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

Cem Sentin
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,

[(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

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