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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

hint Hint:

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 substituting $not stretchy rightwards double arrow x equals fraction numerator negative 3 over denominator 4 end fraction$ 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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