Question

x square minus 11 x + 8 by completing square method

Answer 1

x² - 11x + 8 = 0

x² - 11x = - 8

add both sides, (11/2)²

x² - 11x + (11/2)² = - 8 + (11/2)²

x² -2(11/2).x + (11/2)² = (-32 + 121)/4

( x - 11/2)² = ( 89)/4

take square root both sides ,

(x - 11/2) = ±√189/2

x = 11/2 ± √89/2

hence, ( 11 + √89)/2 and ( 11-√89)/2 are the roots of x² - 11x + 8

Answer 2

x²-11x+8 = 0

x²-11x = -8

adding (11/2)² on both sides,

x²-11x+(11/2)² = -8+(11/2)²

x²-2(x)(11/2)+(11/2)² = -8+121/4

(x-11/2)² = (-32+121)/4

(x-11/2)² = 89/4

take square root on both sides,

√(x-11/2)² = ±√(89/4)

(x-11/2) = ±√89/2

x = 11/2 ± √89/2

x = (11±√89)/2

therefore,the roots of x²-11x+8 are {(11+√89)/2} and {(11-√89)/2}

hope it helps...…