If x-1-1-2- then the value of x2-2 x-3 isA- 3B- 0C- 4D- 1

The correct option is C 4 x = 1/1 + √(2) After rationalization x = 1/1 + √(2)×1 √(2)/1 √(2) x = √(2) 1 So x^2 = 3 2 √(2) ∴ x^2 + 2x + 3 ⇒ (3 2 √(2)) ...

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Standard IX

Mathematics

Multiplication of Numbers with Square Roots

If x=1/1+√2, ...

Question

If $x = \frac{1}{1 + \sqrt{2}},$ then the value of $x^{2} + 2 x + 3$ is

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Solution

The correct option is C
4

$x = \frac{1}{1 + \sqrt{2}}$
After rationalization
$x = \frac{1}{1 + \sqrt{2}} \times \frac{1 - \sqrt{2}}{1 - \sqrt{2}} x = \sqrt{2} - 1 S o x^{2} = 3 - 2 \sqrt{2} ∴ x^{2} + 2 x + 3 \Rightarrow (3 - 2 \sqrt{2}) + 2 (\sqrt{2} - 1) + 3 = 4$

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If x=11+√2, then the value of x2+2x+3 is

The correct option is C 4 x=11+√2 After rationalization x=11+√2×1−√21−√2x=√2−1So x2=3−2√2∴x2+2x+3⇒(3−2√2)+2(√2−1)+3=4

If $x = \frac{1}{1 + \sqrt{2}},$ then the value of $x^{2} + 2 x + 3$ is

The correct option is C
4

$x = \frac{1}{1 + \sqrt{2}}$
After rationalization
$x = \frac{1}{1 + \sqrt{2}} \times \frac{1 - \sqrt{2}}{1 - \sqrt{2}} x = \sqrt{2} - 1 S o x^{2} = 3 - 2 \sqrt{2} ∴ x^{2} + 2 x + 3 \Rightarrow (3 - 2 \sqrt{2}) + 2 (\sqrt{2} - 1) + 3 = 4$