solve for y 2y - 3 = \sqrt{ {3y}^{2} - 10y + 12} absurd answers will be reported!!​

Question

solve for y
2y - 3 =   \sqrt{ {3y}^{2}  - 10y + 12}
absurd answers will be reported!!​

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Euphemia 2 months 2021-07-30T08:09:56+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-07-30T08:11:20+00:00

    Answer:

    y = 3

    Step-by-step explanation:

    2y – 3 = \sqrt{3y^2-10y+12}

    square both sides to remove sqrt bracket

    (2y – 3)^2 = ( \sqrt{3y^2-10y+12} )^2

    simplify both sides

    (2y – 3)(2y – 3) = 3y^2 – 10y + 12

    4y^2 – 12y + 9 = 3y^2 – 10y + 12

    bring all value to left side

    y^2 – 2y – 3 = 0

    factor

    (y – 3)(y + 1)

    solve for y

    y = 3, y = -1

    When plugged back into the equation, only y = 3 is true

    0
    2021-07-30T08:11:35+00:00

    Answer:

    y = 3

    Step-by-step explanation :

    2y - 3 = \sqrt{ 3y² - 10y + 12}

    Swap the sides both of the equation.

    \sqrt{ 3y² - 10y + 12} = 2y - 3

    To remove the brackets of equations square both side and simplify .

    3y² – 10y + 12 = 4y² – 12y + 9

    Move the expression to left-hand side and change its sign.

    3y² – 10y + 12 – 4y² + 12y – 9 = 0

    collect like terms

    3y² – 4y² – 10y + 12y + 12 – 9 = 0

    -y² + 2y + 3 = 0

    Change the sign of expression. because it helps to solve.

    y² – 2y – 3 = 0

    Splits the term -2y

    y² + y 3y – 3 = 0

    Factor out y from the first pair and -3 from second pair of expression.

    y ( y + 1 ) – 3 ( y + 1) = 0

    Factor out y + 1 from the expression.

    ( y + 1 ) ( y – 3 ). = 0

    When product and factors equals 0. at least one factor is 0.

    y + 1 =0

    y – 3 = 0

    Solve for y

    y = -1 and y = 3

    If we plug the 3 as y in the expression we find that y = 3 is the true solution of this expression.

    This equation has one solution which is y = 3.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )