Please check-Reiny

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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

  • Please check-Reiny -

    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.

  • Thank you Reiny -

    Thanks I think I somewhat get it-Thanks again for the explanations

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