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# Solve 2(X^2 + 1/X^2) - (X + 1/X) = 11 - Mathematics

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Sum

Solve 2(x^2 + 1/x^2) - (x + 1/x) = 11

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#### Solution

2(x^2 + 1/x^2) - (x + 1/x) = 11

Let x + 1/x = y

squaring on both side

x^2 + 1/x^2 = y^2 - 2

Putting these values in the given equation

2(y^2 - 2) - y = 11

=> 2y^2 - 4 - y - 11 = 0

=> 2y^2 - y - 15 = 0

=> 2y^2 - 6y + 5y - 15 = 0

=> (y - 3)(2y + 5) = 0

If y - 3 = 0 or 2y + 5  = 0

then y = 3 or y = (-5)/2

=> x + 1/x = 3     or x + 1/x = (-5)/2

=> (x^2 + 1)/x = 3   or (x^2 + 1)/x = (-5)/2

=> x^2 - 3x+ 1 = 0  or 2x^2 + 5x + 2 = 0

=> x = (-3 +- sqrt((-3)^2 - 4(1)(1)))/(2(1)) or 2x^2 + 4x + x + 2 = 0

=> x = (-3 +- sqrt5)/2  or 2x(x + 2) + 1(x + 2) = 0

then x =  -2 and x = (-1)/2`

Concept: Quadratic Equations
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 5 Quadratic Equations
Exercise 5 (E) | Q 9 | Page 66

#### Video TutorialsVIEW ALL [5]

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