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Maths-

General

Easy

Question

Solve the radical equation $square root of 5 x plus 1 end root plus 1 equals x$ . Check for extraneous solutions

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: 7

Complete step by step solution:
Here we have the equation $square root of 5 x plus 1 end root plus 1 equals x$
On squaring, we have $5 x plus 1 equals left parenthesis x minus 1 right parenthesis squared$
$not stretchy rightwards double arrow 5 x plus 1 equals x squared minus 2 x plus 1$
$not stretchy rightwards double arrow x squared minus 2 x minus 5 x plus 1 minus 1 equals 0$
$not stretchy rightwards double arrow x squared minus 7 x equals 0$
⇒ x = 7
On substituting the value of x in the equation, we get
$square root of 5 cross times 7 plus 1 end root plus 1 equals square root of 36 plus 1 equals 6 plus 1 equals 7$
Hence there is no extraneous solution.

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