Solve the equation \(\displaystyle{4}{x}^{{4}}+{3}{x}^{{2}}-{1}={0}\)

aidinacol7

aidinacol7

Answered question

2022-03-23

Solve the equation
4x4+3x21=0

Answer & Explanation

mhapo933its

mhapo933its

Beginner2022-03-24Added 9 answers

Factorize the equation 4x4+3x21=0 and simplify it.
Write 3x2 as the difference of 4x2x2 in the given equation.
Factorize 4x2
Then factorize (x2+1) out of the equation (2) and proceed further.
4x4+3x21=0
4x4+4x2x21=0 (1)
4x2(x2+1)1(x2+1)=0 (2)
(x2+1)(4x21) (3)
Make the brackets equal to zero of equation (3)
x2+1=0
x=±i
4x21=0
x=±12
Thus, the only real solutions to the given equation are x=±12

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