Hi.........may I ask a math question? Trust me its very simple! But I dont get it!?

Question

The equation is squareroot of 3t-14 and plus T=6
name any extraneus solutions of the equation.
what is the solution of the equation?

Answer 1

So it's √(3t - 14) + t = 6?

Then add -t to both sides to get
√(3t - 14) = 6 - t

Square both sides to get rid of square root
3t - 14 = (6-t)^2 = (6-t)(6-t) = 36 - 12t + t^2

Move the 3t - 14 over by adding their opposites
0 = 50 - 15t + t^2

FOIL it
0 = (10-t)(5-t)

so t = 10 or 5

Now plug each into the original equation to see if either or both work. If one doesn't work, it's extraneous.

Answer 2

A squareroot of a number (call it X) is another number (call it y) that, when multiplied by itself (y times y) gives the original number (X).

For example, the square root of 9 = 3 because 3 times 3 = 9.

Here, you have SQRT(3t-14) and you have t=6

if one t is 6, then three t's will be 3*6 = 18

SQRT(3t-14) = SQRT(18-14) = SQRT(4).

What number, when multiplied by itself, gives 4?

2 is such a number (because 2*2 = 4).

-2 is also such a number because (-2)*(-2) = 4.

So there are two solutions.

Sometimes, there are problems where both solutions are valid. For example, if you throw something upward and you want to know after how much time the object is 2 metres above you, there may be two answers: once on the way up and once on the way down (and this is a problem that is solved with a square root).

In mathematics, where functions are defined as having only one solution, we usually pick the positive value. But that will be much later in your program.

Answer 3

6 = (3t-14)^(1/2) + t
6-t = (3t-14)^(1/2) square both sides
(6-t)^2 = 3t-14
t^2-12t+36 = 3t-14 expand
t^2-15t+50 = 0 simplify
(t-10)(t-5) = 0 factor
t = 5,10 solve for zero

Plug answers into the original equation to check:

6 = sqrt(1)+5
6 = 6

6 = sqrt(16) + 10
6 = 4+10
6 = 14
10 is an extraneous solution, because it doesn't actually solve the equation. This is a result of squaring both sides when solving.

So the only right answer is 5.

Answer 4

√(3t -14) +t =6
Domain : 3t -14 ≥ 0 ---> t ≥ 14/3
Domain = [14/3 , +∞ [

√(3t -14) =6-t

squaring both sides (when t ≤ 6, that is only when t ≤ 6 we can square both sides) to get
3t -14 = 36 +t² -12t
t² -15t +50 =0
Discriminant = 225 -4(50) = 25 = 5²
t1 = (15 -5)/2 = 5
t2 = (15 +5)/2 =10 --------> (rejected because it is not ≤ 6)

Conclusion:
only t = 5 is a solution

Answer 5

sub 6 in so you have 3(6)-14 do it works out to be 18-14 which = 4 the square root of 4 is 2
hope that helps