Asked by kim
Solve \sqrt{10-x} + x=8. Enter your solutions in a comma-separated list.
I used the quadratic formula and ended up with-127+-(-215)/2
I used the quadratic formula and ended up with-127+-(-215)/2
Answers
Answered by
Steve
Did you actually try using your values to see whether they satisfied the equation?
√(10-x) + x = 8
√(10-x) = 8-x
10-x = x^2-16x+64
x^2-15x+54 = 0
(x-9)(x-6) = 0
x = 6 or 9
should have showed your work, so we could see what went wrong.
√(10-x) + x = 8
√(10-x) = 8-x
10-x = x^2-16x+64
x^2-15x+54 = 0
(x-9)(x-6) = 0
x = 6 or 9
should have showed your work, so we could see what went wrong.
Answered by
Reiny
However, since both sides were squared, all answers must be checked in the original equation
√(10-x) + x = 8
if x = 6
LS = √4 + 6 = 8 = RS
if x = 9
LS = √1 + 9 = 10 ≠ RS
so the only solution is x = 6
√(10-x) + x = 8
if x = 6
LS = √4 + 6 = 8 = RS
if x = 9
LS = √1 + 9 = 10 ≠ RS
so the only solution is x = 6
Answered by
Steve
I did check the other answer.
Sure enough, √1 + 9 = 10
and I thought, "That's ok."
Good catch. I had expected an extraneous root, and was surprised that there "wasn't" one.
Sure enough, √1 + 9 = 10
and I thought, "That's ok."
Good catch. I had expected an extraneous root, and was surprised that there "wasn't" one.
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