Question

Find the all real roots of the equation (2x^2-3)^2-x^2=0

Answer 1

♠ ANSWER IS IN THE ATTACHMENT PROVIDED.

Answer 2

( 2x^2 - 3 )^2 - x^2 = 0

4 x^4 + 9 - 12 x^2 - x^2 = 0

4 x^4 - 13 x^2 + 9 = 0

4 x^4 - 9 x^2 - 4 x^2 + 9 = 0

x^2 ( 4 x^2 - 9 ) - 1 ( 4 x^2 - 9 ) = 0

( x^2 - 1 ) ( 4 x^2 - 9 ) = 0

{ ( x^2 - 1^2 ) } { (2x)^2 - ( 3 )^2 } = 0

( x - 1 ) ( x + 1 ) ( 2x - 3 ) ( 2x + 3 ) = 0

x - 1 = 0, x + 1 = 0, 2x - 3 = 0, 2x + 3 = 0

x = 1 , x = -1 , x = 3 / 2 , x = - 3 / 2

hence, x = 1 , - 1 , 3 / 2 , - 3 /2 are all real roots of given polynomial.

【 hope it helps 】