√t + 9 + 3 = t?

Question

The answer in the book says 7, but Im not sure how to get that?

Answer 1

t = 16, t = 9

t^½ = t - 12
t = t^2 - 24t + 144
t^2 - 25t + 144 = 0
t = 16, 9

Both check out (of course, this is the quadratic formula we are talking about!) so long as you remember t½ can equal +4 or -4 and +3 or -3.


However...

That does mean 7 is not an answer. But the book isn't likely to be wrong all that often. So... since one has to wonder why it gives you simple addition to do in starting out, one wonders what happens if you left out the parentheses you needed to add when you couldn't group things with the usual bar over the things the radical sign takes effect on. To be a little clearer, what happens if it should be: (t + 9)^½ + 3 = t?

(t + 9)^½ = t - 3 and square each side:
t + 9 = t^2 - 6t + 9 and rearrange to quadratic form:
t^2 - 7t + 0 = 0 and solving:
t = 7, 0

Checking back into the original they both check out as long as one remembers a square root can be the + or - of the numerical portion (i.e.: 0 is the one where that has to be remembered: 9½ = +3 or -3 (7 yields 4 + 3 = 7 if one forgets and one never need notice he forgot.))

Answer 2

√(t + 9) + 3 = t I'm making an educated guess on the ( )
√(t + 9) + 3 = t subtract 3 from each side
√(t+9)=t-3 square both sides
t+9=t^2-6t+9 subtract 9 from each side
t=t^2-6t subtract t from each side
t^2-7t=0
t(t-7)=0
t=0
t-7=0
t=7

check
√(0+9)+3=0
√9+3=0
6=0
so t=0 is NOT a solution
√(7+9)+3=7
√16 + 3=7
4+3=7
7=7
t=7 IS a solution.

Answer 3

Replace t with x^2 to get:

x + 12 = x^2
x^2 - x -12 = 0
(x - 4)(x + 3) = 0

x =4 or x = -3.

So,
t = 16 or t = 9

Answer 4

√t + 9 + 3 = t?

√t = t-12
t=t^2-24t+144

t^2-25t+144=0
t1=(25-7)/2
=9 does not satisfy

t2=(25+7)/2
=16

answer t=16

Answer 5

For the third time: get the radical term by itself on one side, square both sides to get rid of the radical, then solve. In this case you'll end up with a t^2 term, so it will some down to solving a quadratic.

Answer 6

You forgot to group the (t + 9).

Answer 7

i think this is the answer
9+3=t-t^1/2
t=16

12=16-4
12=12

Answer 8

√t + 9 + 3 = t?. let sqrt(t)=x, then
x^2-x-12=0
x=4,-3
t=16,9