Question

If x² - (4/x²) = 3, then ( అయిన ) x = ?

Answer 1

Step-by-step explanation:

Given:-

x² - (4/x²) = 3

To find:-

Find the value of x ?

Solution:-

Given equation is x² - (4/x²) = 3

=> [(x²)(x²)-4]/x² = 3

=> (x⁴-4)/x² = 3

=> x⁴-4 = 3x²

=> x⁴-4-3x² = 0

=> x⁴-3x²-4 = 0

=>x⁴+x²-4x²-4 = 0

=>x²(x²+1) -4(x²+1) = 0

=>(x²+1)(x²-4) = 0

=> x²+1 = 0 or x²-4 = 0

=> x² = -1 or x² = 4

=> x = ±√-1 or x = ±√4

=> x = ±√-1 or x = ±2

=> x = √-1 , -√-1 , -2 , 2 or

=> x = √i² , -√i² , -2 ,2

=> x = i, - i ,-2 ,2

Answer:-

The values of x are √-1 , -√-1 , -2 , 2 or

i, - i ,-2 ,2

Used formulae:-

• a^m×a^n = a^(m+n)
• i² = -1

Used Method:-

• Splitting the middle term

Points to know:-

• If the degree of an equation is 4 then it is called bi-quadratic equation.
• The general form of the bi-quadratic equation is ax⁴+bx³+cx²+dx+e
• A bi-quadratic equation has at most 4 roots