Maths-
General
Easy

Question

Solve the radical equation square root of x plus 1 end root plus 1 equals square root of x plus 3 end root  Check for extraneous solutions

hintHint:

Rearrange the equation and then solve for x.

The correct answer is: 1=3/2


    Complete step by step solution:
    Here we have the equation square root of x plus 1 end root plus 1 equals square root of x plus 3 end root

    not stretchy rightwards double arrow square root of x plus 3 end root equals 1 plus square root of x plus 1 end root
    On squaring both the sides, we have x plus 3 equals left parenthesis 1 plus square root of x plus 1 end root right parenthesis left parenthesis 1 plus square root of x plus 1 end root right parenthesis
    On subtracting x and 2 on both the sides, we get
    not stretchy rightwards double arrow 1 equals 2 square root of x plus 1 end root
    On squaring both the sides, we get
    = 4(x + 1)
    ⇒ 1 = 4x + 4
    not stretchy rightwards double arrow x equals fraction numerator negative 3 over denominator 4 end fraction
    Here, on substitutingnot stretchy rightwards double arrow x equals fraction numerator negative 3 over denominator 4 end fraction in given equation we get
    not stretchy rightwards double arrow space square root of fraction numerator negative 3 over denominator 4 end fraction plus 1 end root plus 1 equals square root of fraction numerator negative 3 over denominator 4 end fraction plus 3 end root
    not stretchy rightwards double arrow space square root of 1 fourth end root plus 1 equals square root of 9 over 4 end root
    not stretchy rightwards double arrow 1 half plus 1 equals 3 over 2
    Hence no extraneous solution.

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