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Maths-

SAT

Easy

Question

$x plus 1 equals fraction numerator 2 over denominator x plus 1 end fraction$
In the equation above, which of the following is a possible value of x + 1 ?

$1 - \sqrt{2}$
$\sqrt{2}$
2
4

The correct answer is: $square root of 2$

Given $x plus 1 equals fraction numerator 2 over denominator x plus 1 end fraction$
(x + 1)(x +1) = 2
x² + x + x + 1 = 2
x²+ 2x + 1 = 2
x²+ 2x + 1 – 2 = 0
x² + 2x – 1 = 0
The above Quadratic equation cannot be factorized. Thus, quadratic formula can be applied.
$x equals fraction numerator open square brackets negative b plus-or-minus square root of b squared minus 4 a c end root close square brackets over denominator 2 a end fraction$
a = 1
b = 2
c = -1
$x equals fraction numerator open parentheses negative 2 plus-or-minus square root of 2 squared minus 4 left parenthesis 1 right parenthesis left parenthesis negative 1 right parenthesis end root close parentheses over denominator 2 left parenthesis 1 right parenthesis end fraction$
= $fraction numerator negative 2 plus-or-minus square root of 4 plus 4 end root over denominator 2 end fraction$
= $fraction numerator negative 2 plus-or-minus square root of 8 over denominator 2 end fraction$
$square root of 8 equals square root of 4 cross times 2 end root equals 2 square root of 2$
$x equals fraction numerator negative 2 plus-or-minus 2 square root of 2 over denominator 2 end fraction$
$x equals negative 1 plus-or-minus square root of 2$
$x equals negative 1 plus square root of 2 text and end text x equals negative 1 minus square root of 2$
$x equals negative 1 plus square root of 2$
$x plus 1 equals negative 1 plus square root of 2 plus 1 equals square root of 2$

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