Could you check these two problems?
3sqrt (y+2) = 3 is y = 25
Answers were: true or false
I said true because I did it like this
Square both sides=y + 2 = 3^3
y+2 = 27
y = 25
and sqrt (2y-6) = 3-y for y
answes are:
no solution
5
3,5
3
I said 3 because I did it like this:
8y -15 + y^2 = 0
y^2 + 8y -15 =0
(y-5) (y+3) = 0
Y = 3,5 but five doesn't work only 3
Can you please check-I didn't put all the steps for the second one-it was too long
you forgot about the 3 in front of 3√(y+2) when you squared
should be
9(y+2) = 9
y+2 = 1
y = -1
check:
LS = 3√(-1+2) = 3√1 = 3
RS = 3
so y = -1
for the second watch your simplifation, my final quadratic was
y^2 - 8y + 15 = 0
(y-3)(y-5) = 0
y = 3 or y = 5
You should have had y = -3
you are right in the conclusion, only x = 3 verifies.
Thanks I think I somewhat get it-Thanks again for the explanations
Let's check both problems to confirm the answers:
1. 3√(y+2) = 3
To solve this equation, you squared both sides, which is not the correct approach. Here's the correct way to solve it:
Cube both sides of the equation to eliminate the cube root: (3√(y+2))^3 = 3^3
This gives you: y + 2 = 27
Now subtract 2 from both sides to isolate y: y = 27 - 2
Simplifying it further, y = 25
So, the correct answer is y = 25. Therefore, your answer of "true" for y = 25 is correct.
2. √(2y-6) = 3 - y
Your solutions for this problem are incorrect. Here's the correct approach:
Square both sides of the equation to eliminate the square root: (√(2y-6))^2 = (3 - y)^2
Simplifying it, you get: 2y - 6 = 9 - 6y + y^2
Rearranging the equation, you have: y^2 + 8y - 15 = 0
Now, you correctly factorized the quadratic equation: (y - 5)(y + 3) = 0
From here, you have two potential solutions: y - 5 = 0 or y + 3 = 0
Solving these equations, you get y = 5 or y = -3
However, you correctly observed that y = 5 doesn't satisfy the original equation. Therefore, the correct solution is y = -3.
So, the correct answer for the second problem is y = -3. Therefore, your answer of "3" is incorrect.
To summarize:
Problem 1: Your answer of y = 25 is correct.
Problem 2: The correct answer is y = -3, not 3.