Question

Factorize =4x^4+3x^2+9​

Answer 1

Solution:-

Given

4x⁴+3x²+9

let x²= y

=> 4y²+3y+9

=> y =[ -3±√ ( 9-4×4×9)] / 8

=> y= [ -3±√(- 135)] / 8

=> y = [ -3±3√(-15)] / 8

=> y = (3/8) [ -1 ±√(-15)]

substituting y = x²

=> x² = (3/8) [ -1 ±√(-15)]

Then

_____________

=> x = ± √( 3/8) [ -1±√(-15)]

Answer

factorisation:-

4x⁴+3x²+9

= (2x²)²+(3)²+12x²-12x²+3x²

= (2x²+3)²-(3x)²

= (2x²+3x+3) ( 2x²-3x+3)