Maths-
General
Easy

Question

Solve the radical equation square root of 15 minus x end root minus square root of 6 x end root equals negative 3

Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = 6/49


    Complete step by step solution:
    Here we have the equation square root of 15 minus x end root minus square root of 6 x end root equals negative 3
    not stretchy rightwards double arrow square root of 15 minus x end root equals negative 3 plus square root of 6 x end root
    On squaring both the sides, we have 15 minus x equals left parenthesis negative 3 plus square root of 6 x end root right parenthesis left parenthesis negative 3 plus square root of 6 x end root right parenthesis
    not stretchy rightwards double arrow 15 minus x equals 9 minus 6 square root of 6 x end root plus 6 x
    On subtracting, 6x and 9 from both the sides, we get
    not stretchy rightwards double arrow 6 minus 7 x equals negative 6 square root of 6 x end root
    On squaring both the sides, we get
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell space space space space space space space space space space 49 x squared minus 84 x plus 36 equals 216 x end cell row cell not stretchy rightwards double arrow 49 x squared minus 300 x plus 36 equals 0 end cell end table
    Now, this is a quadratic equation with a = 49, b = -300, c = 36
    Roots can be found with, x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    x equals fraction numerator 300 plus-or-minus square root of 90000 minus 4 cross times 49 cross times 36 end root over denominator 2 cross times 49 end fraction
    On solving, we get x equals 6 comma 6 over 49
    Here, on substituting x equals 6 text  or  end text 6 over 49 in given equation we get
    square root of 15 minus 6 end root minus square root of 6 cross times 6 end root equals negative 3
    not stretchy rightwards double arrow square root of 9 minus square root of 36 equals 3 minus 6 equals negative 3
    Hence x = 6 works.
    Now, square root of 15 minus 6 over 49 end root minus square root of 6 cross times 6 over 49 end root equals negative 3
    not stretchy rightwards double arrow 27 over 7 minus 6 over 7 equals 21 over 7 equals 3 not equal to negative 3
    Here x equals 6 over 49 does not work.
    Hence x equals 6 over 49 is an extraneous solution.

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