- #1
Rectifier
Gold Member
- 313
- 4
1. The problem
When is the following equation true
## \sqrt{c^2+14c+49} = c + 7##
a) for all real c
b) for ## c \geq -7 ##
c) for ## c < -7##
d) c > 0
e) c < 0
The attempt 1
I know that the root of ## c^2+14c+49 = 0 ## is ## c = -7 ## and that this sqr-root is only defined for positive numbers. Thus the equation is true only when the stuff below the root is positive. But that stuff is always positive...
The attempt 2
## \sqrt{c^2+14c+49} = c + 7 \\ \sqrt{(c+7)^2} = c + 7 \\ c+7 = c + 7 \\ ##
Thus this equation is true for all real c:s. But somehow this is wrong.
When is the following equation true
## \sqrt{c^2+14c+49} = c + 7##
a) for all real c
b) for ## c \geq -7 ##
c) for ## c < -7##
d) c > 0
e) c < 0
The attempt 1
I know that the root of ## c^2+14c+49 = 0 ## is ## c = -7 ## and that this sqr-root is only defined for positive numbers. Thus the equation is true only when the stuff below the root is positive. But that stuff is always positive...
The attempt 2
## \sqrt{c^2+14c+49} = c + 7 \\ \sqrt{(c+7)^2} = c + 7 \\ c+7 = c + 7 \\ ##
Thus this equation is true for all real c:s. But somehow this is wrong.