How do you solve sqrt( x^2+7)=x+1√x2+7=x+1?
1 Answer
May 8, 2016
Explanation:
First square both sides, noting that squaring may introduce spurious solutions...
x^2+7 = (x+1)^2 = x^2+2x+1x2+7=(x+1)2=x2+2x+1
Subtract
7 = 2x+17=2x+1
Subtract
6 = 2x6=2x
Divide both sides by
x = 3x=3
Check that this is a solution of the original equation:
sqrt(x^2+7) = sqrt(3^2+7) = sqrt(9+7) = sqrt(16) = 4 = 3+1 = x+1√x2+7=√32+7=√9+7=√16=4=3+1=x+1