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    Maths-
    General
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    Question

    Solve the radical equation square root of x plus 4 end root minus square root of 3 x end root equals negative 2. Check for extraneous solutions

    hintHint:

    Rearrange the equation and then solve for x.

    The correct answer is: ⇒ x = 12

      Complete step by step solution:
      Here we have the equation square root of x plus 4 end root minus square root of 3 x end root equals negative 2
      not stretchy rightwards double arrow square root of x plus 4 end root equals negative 2 plus square root of 3 x end root
      On squaring both the sides, we have x plus 4 equals left parenthesis negative 2 plus square root of 3 x end root right parenthesis left parenthesis negative 2 plus square root of 3 x end root right parenthesis
      not stretchy rightwards double arrow x plus 4 equals 4 minus 4 square root of 3 x end root plus 3 x
      On subtracting, 3x and 4 from both the sides, we get
      not stretchy rightwards double arrow negative 2 x equals negative 4 square root of 3 x end root
      On squaring both the sides, we get
      table attributes columnspacing 1em end attributes row cell space space space space space space space space space space 4 x squared equals 16 cross times 3 x end cell row cell not stretchy rightwards double arrow x equals 12 end cell end table

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