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What is the value of x+y ?

## Roots of an Equation

(3 + 2√2)(x2 - 3) + (3 - 2√2)(x2 - 3) = b which of the following can be one of the roots of the equation
1. 2
2. √2
3. -√2
4. All of the above

Choice D. All of the above

## Detailed Solution

(3 + 2√2)(x2 - 3) be y.

Now, (3 + 2√2)(x2 - 3) = ($\frac {(3-2√2)(3+2√2)}{(3+2√2)}$)(x2 - 3) = ($\frac {9-8}{(3+2√2)}$)(x2 - 3) = ($\frac {1}{(3+2√2)}$)(x2 - 3) = $\frac {1}{y}$

∴ Equation can be written as:-

y + $\frac {1}{y}$ = b

y2 + 1 = by

y2 – by + 1 = 0

The roots of the equation are:-

y = $\frac {(b±\sqrt{36-4})}{2}$

= $\frac {(b ± \sqrt{32})}{2}$

= 3 ± 2√2

∴ Case 1 = (3 + 2√2)(x2 - 3) = 3+2√2

=) x2 – 3 = 1

=) x2 = 4 =) x = ± 2

Case 2 = (3 + 2√2)(x2 - 3) = 3-2√2

=) x2 – 3 = -1

=) x2 = 2 =) x = ± √2

Correct Answer: All of the above

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