Question

x^4-11x^2+1 slove the Factor
​

Answer 1

Topic

Factorisation

Given Equation

x⁴ - 11x² + 1

Formula used

a⁴ -2a²b + b² = ( a² - b )²

a² - b² = ( a + b )( a - b )

Solving

Method 1 ( Hard )

x⁴ - 11x² + 1

Add and Subtract ( 11/2 )² to make it a perfect square.

x⁴ - 11x² + (11/2)² - ( 11/2)² + 1

( x² - 11/2 )² - ( 121/4 ) + 1

( x² - 11/2 )² - ( 121/4 ) + 1

( x² - 11/2 )² - [ ( √117 ) / 2 ]²

Now, apply second mentioned formula.

[ x² - ( 11 - √117 ) / 2 ][ x² - ( 11 + √117 ) / 2 ]

Method 2 ( Easy )

x⁴ - 11x² + 1

x⁴ - 2x² + 1 - 9x²

Make perfect square then apply second mentioned formula.

( x² - 1 )² - ( 3x )²

( x² - 1 - 3x )( x² - 1 + 3x )

Answer

So, answer can be both but easiest one is

( x² - 1 - 3x )( x² - 1 + 3x )