<PRE><B>Question 567489</B>
square root of y+8 minus square root of y-6 equals -3,
:
{{{sqrt(y+8) - sqrt(y-6)}}} = -3
:
{{{sqrt(y+8) = sqrt(y-6)}}} - 3
square both sides
y + 8 = [{{{sqrt(y-6)}}} - 3]^2
FOIL the right side
y + 8 = {{{(y-6) - 3sqrt(y-6) - 3sqrt(y-6) + 9}}}
:
y + 8 = y + 3 - {{{6sqrt(y-6)}}}
:
y + 8 = y + 3 - {{{6sqrt(y-6)}}}
y - y + 8 - 3 = {{{6sqrt(y-6)}}}
5 = {{{6sqrt(y-6)}}}
square both side again
25 = 36(y-6)
25 = 36y - 216
25 + 216 = 36y
241 = 36y
y = {{{241/36}}}
y = 6.7 which about what you got, but the trouble is if we substitute this in the original problem we get a +3 not -3, therefore there is no solution
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