Maths-
General
Easy

Question

Neil said that – 3 and 6 are the solutions to square root of 3 x plus 18 end root equals x. What error did Neil make?

Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = -3


    Complete step by step solution:
    Here we have the equation square root of 3 x plus 18 end root equals x
    On squaring both the sides, we have 3 x plus 18 equals x squared
    On rearranging, we have x squared minus 3 x minus 18 equals 0
    Now, this is a quadratic equation with a = 1, b = -3, c = -18
    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 3 plus-or-minus square root of 9 minus 4 cross times 1 cross times negative 18 end root over denominator 2 cross times 1 end fraction
    On solving, we get x = 6, -3
    Here, on substituting x = 6 or -3 in given equation we get

    square root of 3 cross times 6 plus 18 end root equals 6

    not stretchy rightwards double arrow square root of 18 plus 18 end root equals square root of 36 equals 6

    Hence x = 6 works.

    Now, square root of 3 cross times negative 3 plus 18 end root equals negative 3
    not stretchy rightwards double arrow square root of negative 9 plus 18 end root equals square root of 9 not equal to negative 3
    Hence x = -3 is an extraneous solution.
    The error is that, one of the solutions, x = -3 is an extraneous solution.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.