Maths-
General
Easy

Question

Solve the radical equation 2 x equals square root of 17 x minus 15 end root Check for extraneous solutions

hintHint:

Rearrange the equation and then solve for x.

The correct answer is: Hence no extraneous solution


    Complete step by step solution:
    Here we have the equation 2 x equals square root of 17 x minus 15 end root
    On squaring both the sides, we have left parenthesis 2 x right parenthesis squared equals left parenthesis square root of 17 x minus 15 end root right parenthesis squared

    not stretchy rightwards double arrow 4 x squared equals 17 x minus 15
    On rearranging, we have 4 x squared minus 17 x plus 15 equals 0
    Now, this is a quadratic equation with a = 4, b =-17, c = 15
    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 17 plus-or-minus square root of 289 minus 4 cross times 4 cross times 15 end root over denominator 2 cross times 4 end fraction
    On solving, we get x equals 3 comma 5 over 4
    Here, on substituting x equals 3 text  or  end text 5 over 4 in given equation we get
    2 cross times 3 equals square root of 17 cross times 3 minus 15 end root
    not stretchy rightwards double arrow 6 equals square root of 36 equals 6
    Hence x = 3 works.
    Now equals 2 cross times 5 over 4 equals square root of 17 cross times 5 over 4 minus 15 end root
    not stretchy rightwards double arrow 5 over 2 equals square root of 25 over 4 end root equals 5 over 2
    Hence x equals 5 over 4 works.
    Hence no extraneous solution.

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