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

2 Answers
Manasvini Nittala
Nov 8, 2017

the answer is a=4a=4

Explanation:

the given equation is sqrt(a+21)-1=sqrt(a+12)√a+21−1=√a+12
squaring on both sides we get
a+21+1-2sqrt(a+21)=a+12a+21+1−2√a+21=a+12
simplifying we get 2sqrt(a+21)=10rArrsqrt(a+21)=52√a+21=10⇒√a+21=5
squaring on both sides we get
a+21=25rArra=4a+21=25⇒a=4

Cem Sentin
Nov 8, 2017

a=4a=4

Explanation:

sqrt(a+21)-1=sqrt(a+12)√a+21−1=√a+12

sqrt(a+21)-sqrt(a+12)=1√a+21−√a+12=1

After using difference of squares identity,

[(a+21)-(a+12)]/[sqrt(a+21)-sqrt(a+12)]=9/1(a+21)−(a+12)√a+21−√a+12=91

sqrt(a+21)+sqrt(a+12)=9√a+21+√a+12=9

Hence,

sqrt(a+21)+sqrt(a+12)+sqrt(a+21)-sqrt(a+12)=9+1√a+21+√a+12+√a+21−√a+12=9+1

2sqrt(a+21)=102√a+21=10

sqrt(a+21)=5√a+21=5

a+21=25a+21=25

a=4a=4

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