Question

x^2×(x^2-2x+1)=36. How to solve ​

Answer 1

Solution :

x²( x² - 2x + 1) = 36

=> x⁴ - 2x³ + x² = 36

=> x⁴ - 2x³ + x² - 36 = 0

=> x⁴ + x³ - 3x³ + 4x² - 3x² - 12x - 36 = 0

=> x⁴ + x³ + 4x² - 3x³ - 3x² - 12x - 36 = 0

=> x( x³ + x² + 4x + 12) - 3(x³ + x² + 4x + 12) = 0

=> ( x - 3)( x³ + x² + 4x + 12) = 0

=> ( x - 3)( x³ + 2x² - x² + 6x - 2x + 12) = 0

=> ( x - 3)( x³ - x² + 6x + 2x² - 2x + 12 ) = 0

=> ( x - 3)[ x( x² - x + 6 ) + 2( x² - 6x + 6) ] = 0

=> ( x - 3)(x + 2)( x² - x + 6) = 0

Thus , the roots become :

=> • x = -2

• x = 3

• x = ½ ± √23í/2

This is the required answer .

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