SOLUTION: solve the equation 3 + square root z-7 close quare root = square root z+8 close square root

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Question 762462: solve the equation 3 + square root z-7 close quare root = square root z+8 close square root
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3+%2B+sqrt%28z-7%29+=+sqrt+%28z%2B8%29

3+=+sqrt+%28z%2B8%29-sqrt%28z-7%29+.....square both sides

3%5E2+=+%28sqrt+%28z%2B8%29-sqrt%28z-7%29%29%5E2+
9+=+%28sqrt+%28z%2B8%29%29%5E2-2sqrt+%28z%2B8%29sqrt%28z-7%29%2B%28sqrt%28z-7%29%29%5E2+
9+=+z%2B8-2sqrt+%28z%2B8%29sqrt%28z-7%29%2Bz-7+...........since sqrt+%28z%2B8%29sqrt%28z-7%29=sqrt%28%28z%2B8%29%28z-7%29%29, we will have

9+=+2z%2B1-2sqrt%28%28z%2B8%29%28z-7%29%29+

2sqrt%28%28z%2B8%29%28z-7%29%29+=+2z%2B1-9+

2sqrt%28%28z%2B8%29%28z-7%29%29+=+2z-8+.... both sides divide by 2
sqrt%28%28z%2B8%29%28z-7%29%29+=+z-4+.....square both sides

%28sqrt%28%28z%2B8%29%28z-7%29%29%29%5E2+=+%28z-4%29%5E2+
%28z%2B8%29%28z-7%29+=+z%5E2-8z%2B16+
z%5E2%2B8z-7z-56+=+z%5E2-8z%2B16+
cross%28z%5E2%29%2Bz-56+=+cross%28z%5E2%29-8z%2B16+
z-56+=+-8z%2B16+
z%2B8z=+56%2B16+
9z=+72+
z=+72%2F9+
z=+8+