SOLUTION: a student opens a mathematics book to two facing pages. The product of the page numbers is 506. Find the page numbers. page #1= Page #2=

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Question 335961: a student opens a mathematics book to two facing pages. The product of the page numbers is 506. Find the page numbers. page #1= Page #2=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"a student opens a mathematics book to two facing pages. The product of the page numbers is 506" means that x%28x%2B1%29=506


x%28x%2B1%29=506 Start with the given equation.


x%5E2%2Bx=506 Distribute


x%5E2%2Bx-506=0 Subtract 506 from both sides.


Notice that the quadratic x%5E2%2Bx-506 is in the form of Ax%5E2%2BBx%2BC where A=1, B=1, and C=-506


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-506%29+%29%29%2F%282%281%29%29 Plug in A=1, B=1, and C=-506


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-506%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--2024+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-506%29 to get -2024


x+=+%28-1+%2B-+sqrt%28+1%2B2024+%29%29%2F%282%281%29%29 Rewrite sqrt%281--2024%29 as sqrt%281%2B2024%29


x+=+%28-1+%2B-+sqrt%28+2025+%29%29%2F%282%281%29%29 Add 1 to 2024 to get 2025


x+=+%28-1+%2B-+sqrt%28+2025+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+45%29%2F%282%29 Take the square root of 2025 to get 45.


x+=+%28-1+%2B+45%29%2F%282%29 or x+=+%28-1+-+45%29%2F%282%29 Break up the expression.


x+=+%2844%29%2F%282%29 or x+=++%28-46%29%2F%282%29 Combine like terms.


x+=+22 or x+=+-23 Simplify.


So the possible solutions are x+=+22 or x+=+-23

Ignore the negative answer as negative page numbers don't make sense.


So the pages are 22 and 23


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Jim