If x= 2+√3/2-√3.show that x^2-14x+1=0
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x = ( 2 + √3)/( 2 - √3)
x = (2 + √3)(2 + √3)/( 2 - √3)(2 + √3)
x = (2 + √3)²/(2² -√3²)
x = ( 2² + √3² + 4√3)/( 4 - 3)
x = ( 7 + 4√3)
x - 7 = 4√3
take sqaure both sides,
(x - 7)² = (4√3)²
x² - 14x + 49 = 4√3 × 4√3 = 48
x² - 14x + 49 - 48 = 0
x² - 14x +1 = 0
hence, proved//
x = (2 + √3)(2 + √3)/( 2 - √3)(2 + √3)
x = (2 + √3)²/(2² -√3²)
x = ( 2² + √3² + 4√3)/( 4 - 3)
x = ( 7 + 4√3)
x - 7 = 4√3
take sqaure both sides,
(x - 7)² = (4√3)²
x² - 14x + 49 = 4√3 × 4√3 = 48
x² - 14x + 49 - 48 = 0
x² - 14x +1 = 0
hence, proved//
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