Linear and Quadratic Equations

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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

 

  • Correct Answer
    Choice D. All of the above

Detailed Solution

(3 + 2√2)(x2 - 3) be y.

Now, (3 + 2√2)(x2 - 3) = ()(x2 - 3) = ()(x2 - 3) = ()(x2 - 3) =

∴ Equation can be written as:-

y + = b

y2 + 1 = by

y2 – by + 1 = 0

The roots of the equation are:-

y =

=

= 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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Solving equations well is an integral part to cracking any competitive exam. Get cartloads of practice on these two topics.