How do you solve sqrtx- sqrt(x-5)=1?

1 Answer
R V SUBBARAO
Oct 13, 2015

x = 9

Explanation:

sqrt (x) -sqrt(x-5) = 1 equation 1

multiply both sides with sqrt (x) +sqrt(x-5)

(sqrt (x) -sqrt(x-5)) (sqrt (x) +sqrt(x-5)) = 1(sqrt (x) +sqrt(x-5))

L H S is in the form of (a+b)(a-b) = a^2 -b^2

(sqrt(x))^2 - (sqrt(x-5))^2 = sqrt (x) +sqrt (x-5)
x - (x-5) =sqrt (x) +sqrt(x-5)
x-x+5 = (sqrt (x) +sqrt(x-5))
5 = sqrt (x) +sqrt(x-5) equation 2

Solve equation 1 and 2 for x

sqrt (x) -sqrt(x-5) = 1 equation 1

sqrt (x) +sqrt(x-5) = 5 equation 2

Sum of equation 1 & 2

2sqrt(x) = 6
sqrt(x) = 6/2 = 3
Squaring on both side to get x

x = 9

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