Solve each of the following equations: x² + x + 1/√2 = 0

Solution:

The given quadratic equation is x² - x + 1/√2 = 0

This equation can also be written as √2x² - √2x + 1 = 0

On comparing the given equation with ax² + bx + c = 0,

We obtain a = √2, b = - √2, and c = 1

Therefore, the discriminant of the given equation is

D = b² - 4ac

= (- √2)² - 4 x √2 x 1

= 2 - 4√2

Hence, the required solutions are

(- b ± √D)/2a = (- (√2) ± √2 - 4√2)/(2 x √2)

= (- √2 ± √2(1 - 2√2)) / (2√2)

= [- 1 ± (√2√2 - 1)i] / 2 [∵ √- 1 = i]

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NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.3 Question 9

Solve each of the following equations: x² - x + 1/√2 = 0

Summary:

A complex equation x² - x + 1/√2 = 0 is given. We have found that the solutions of the equation are [- 1 ± (√2√2 - 1)i] / 2