How do you solve #sqrt(x-15)=3-sqrtx# and check the solution?

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Answer 1 · 2017-03-16T17:18:16

Please see the link to WorlframAlpha; it will tell you that No solutions exist.

Before beginning, add the restriction that x must be greater than or equal to 15:

#sqrt(x-15)=3-sqrtx;x >=15#

Add #sqrtx# to both sides:

#sqrt(x-15)+sqrtx=3;x >=15#

Square both sides:

#x- 15 + 2sqrt(x-15)sqrtx + x=9;x >=15#

Add #15 - 2x# to both sides:

#2sqrt(x-15)sqrtx=26 - 2x;x >=15#

Divide both sides by 2:

#sqrt(x-15)sqrtx=13 - x;x >=15#

Square both sides:

#(x-15)x=169 - 26x + x^2;x >=15#

#x^2-15x=169 - 26x + x^2;x >=15#

#-15x=169 - 26x;x >=15#

#11x = 169;x>=15#

#x = 15.36;x>=15#

But if you substitute this solution into the original equation you do not obtain equality; No solutions exist.