Given x*y=xy-2x-2y+6, x*2=2, calculate -2009*-2008*-----*-1*0*1*----2009?
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,349 answers
starTop subjects are Math, Science, and Business
You should use the information provided by the problem `x*2 = 2` , hence, you may group the terms around the term 2 such that:
`((-2009)*......*(-1)*0*1)*2*(3*4*...*2009)`
Reasoning by analogy yields that `((-2009)*......*(-1)*0*1)*2 = 2.`
You should prove that the given law of composition is associative, hence, it satisfies the associative law such that:
`(x*y)*z= x*(x*z)`
You need to use the following form of the law of composition, such that:
`x*y = (x-2)(y-2) + 2`
`(x*y)*z = ((x-2)(y-2) + 2)*z = ((x-2)(y-2) + 2 - 2)(z-2) + 2`
`(x*y)*z = (x-2)(y-2)(z-2) + 2`
`y*z = (y-2)(z-2) + 2`
`x*(y*z) = x*((y-2)(z-2) + 2)`
`x*(y*z) = (x-2)((y-2)(z-2) + 2 - 2) + 2`
You need to evaluate if `(x*y)*z = x*(y*z)` such that:
`(x-2)(y-2)(z-2) + 2 = (x-2)((y-2)(z-2)) + 2`
Reducing 2 both sides yields:
`(x-2)(y-2)(z-2) = (x-2)(y-2)(z-2)`
Since the law is associative and commutative, hence `x*2 = 2*x = 2.`
Reasoning by analogy yields:
`2*(3*4*...*2009) = 2`
Hence, evaluating the expression `((-2009)*......*(-1)*0*1)*2*(3*4*...*2009), ` using the information provided by the problem, yields `((-2009)*......*(-1)*0*1)*2*(3*4*...*2009) = 2.`
Related Questions
- Calculate (sin x)^2 + sin (2x)=0?
- 1 Educator Answer
- x+2y=1 2x+y=8 find x and y
- 2 Educator Answers
- Calculate limit (x^2+2x+1)/(2x^2-2x-1), x->+infinity
- 1 Educator Answer
- x^2y+xy^2=6
- 1 Educator Answer
- x-2y=-4 2x-y=1
- 2 Educator Answers
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.