1. let A = 2  3  and f(x)= x.x-4x+7. show that f(A)=0. use this result to find A.A.A.A.A.
             -1 2

Asked by science field | 9th May, 2015, 04:21: PM

Expert Answer:

G i v e n space t h a t space A equals open square brackets table row 2 3 row cell negative 1 end cell 2 end table close square brackets space a n d space f open parentheses x close parentheses equals x times x minus 4 x plus 7 W e space n e e d space t o space s h o w space t h a t space f open parentheses A close parentheses equals 0 S i n c e space f open parentheses x close parentheses equals x times x minus 4 x plus 7 comma f open parentheses A close parentheses equals A times A minus 4 A plus 7 I rightwards double arrow f open parentheses A close parentheses equals open square brackets table row 2 3 row cell negative 1 end cell 2 end table close square brackets times open square brackets table row 2 3 row cell negative 1 end cell 2 end table close square brackets minus 4 open square brackets table row 2 3 row cell negative 1 end cell 2 end table close square brackets plus 7 open square brackets table row 1 0 row 0 1 end table close square brackets rightwards double arrow f open parentheses A close parentheses equals open square brackets table row cell 2 cross times 2 plus 3 cross times open parentheses negative 1 close parentheses end cell cell 2 cross times 3 plus 3 cross times 2 end cell row cell negative 1 cross times 2 plus 2 cross times open parentheses negative 1 close parentheses end cell cell negative 1 cross times 3 plus 2 cross times 2 end cell end table close square brackets minus open square brackets table row 8 12 row cell negative 4 end cell 8 end table close square brackets plus 7 open square brackets table row 1 0 row 0 1 end table close square brackets rightwards double arrow f open parentheses A close parentheses equals open square brackets table row 1 12 row cell negative 4 end cell 1 end table close square brackets minus open square brackets table row 8 12 row cell negative 4 end cell 8 end table close square brackets plus 7 open square brackets table row 1 0 row 0 1 end table close square brackets rightwards double arrow f open parentheses A close parentheses equals open square brackets table row cell 1 minus 8 end cell cell 12 minus 12 end cell row cell negative 4 plus 4 end cell cell 1 minus 8 end cell end table close square brackets plus 7 open square brackets table row 1 0 row 0 1 end table close square brackets rightwards double arrow f open parentheses A close parentheses equals open square brackets table row cell negative 7 end cell 0 row 0 cell negative 7 end cell end table close square brackets plus open square brackets table row 7 0 row 0 7 end table close square brackets rightwards double arrow f open parentheses A close parentheses equals open square brackets table row cell negative 7 plus 7 end cell cell 0 plus 0 end cell row cell 0 plus 0 end cell cell negative 7 plus 7 end cell end table close square brackets rightwards double arrow f open parentheses A close parentheses equals open square brackets table row 0 0 row 0 0 end table close square brackets T h u s comma space w e space h a v e comma space f open parentheses A close parentheses equals A times A minus 4 A plus 7 I equals 0 rightwards double arrow A times A equals 4 A minus 7 I rightwards double arrow A squared equals 4 A minus 7 I rightwards double arrow A times A times A equals A times open parentheses 4 A minus 7 I close parentheses rightwards double arrow A times A times A equals 4 A squared minus 7 A rightwards double arrow A cubed equals 4 open parentheses 4 A minus 7 I close parentheses minus 7 A rightwards double arrow A cubed equals 16 A minus 28 I minus 7 A rightwards double arrow A cubed equals 9 A minus 28 I rightwards double arrow A times A times A times A equals A open parentheses 9 A minus 28 I close parentheses rightwards double arrow A times A times A times A equals 9 A squared minus 28 A rightwards double arrow A times A times A times A equals 9 open parentheses 4 A minus 7 I close parentheses minus 28 A rightwards double arrow A to the power of 4 equals 36 A minus 63 I minus 28 A rightwards double arrow A to the power of 4 equals 8 A minus 63 I rightwards double arrow A times A times A times A times A equals A open parentheses 8 A minus 63 I close parentheses rightwards double arrow A times A times A times A times A equals 8 A squared minus 63 A rightwards double arrow A times A times A times A times A equals 8 open parentheses 4 A minus 7 I close parentheses minus 63 A rightwards double arrow A times A times A times A times A equals 32 A minus 56 I minus 63 A rightwards double arrow A times A times A times A times A equals negative 31 A minus 56 I rightwards double arrow A to the power of 5 equals negative 31 open square brackets table row 2 3 row cell negative 1 end cell 2 end table close square brackets minus 56 open square brackets table row 1 0 row 0 1 end table close square brackets rightwards double arrow A to the power of 5 equals open square brackets table row cell negative 62 end cell cell negative 93 end cell row 31 cell negative 62 end cell end table close square brackets minus open square brackets table row 56 0 row 0 56 end table close square brackets rightwards double arrow A to the power of 5 equals open square brackets table row cell negative 62 minus 56 end cell cell negative 93 end cell row 31 cell negative 62 minus 56 end cell end table close square brackets rightwards double arrow A to the power of 5 equals open square brackets table row cell negative 118 end cell cell negative 93 end cell row 31 cell negative 118 end cell end table close square brackets

Answered by Vimala Ramamurthy | 11th May, 2015, 12:33: PM