#sqrt (4a + 29) = 2 sqrt (a) + 5? #solve the equations.

1 Answer
shr
Apr 18, 2017

#a = 1/25#

Explanation:

#sqrt(4a+29) = 2sqrt(a) + 5#

Restrictions:
1. #4a + 29 >= 0# or #a >= -29/4#
2. #a >= 0#

Combining the two restrictions for common segments, you get #a>=0#

#(sqrt(4a+29))^2 = (2sqrt(a) + 5)^2#
#4a+29 = 4a + 20sqrt(a) + 25#
#20sqrt(a)= 4#
#sqrt(a)=1/5#
#(sqrt(a))^2=(1/5)^2#
#:.a = 1/25#
This solution satisfies the restriction, thus is valid.

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