Question

if x^2-2x+1=2x than prove that x^8-194x^4+1=0​

Answer 1

Question , x² - 2x + 1 = 2x

TO PROVE :

${x}^{8} - 194 {x}^{4} + 1 = 0$

SOLUTION :

x² - 2x + 1 = 2x

• x² + 1 = 4x

Squaring both sides ,

( x² + 1 )² = (4x)²

• x⁴ + 1 + 2x² = 16x²

• x⁴ + 1 = 14x²

Squaring both sides ,

( x⁴ + 1 )² = ( 14x²)²

• x^8 + 1 + 2x⁴ = 196x⁴

• x^8 - 194 x⁴ + 1 = 0

Proved!

Fomulas used , ( a+b )² = a² + b² + 2ab.