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n(n + 1) and (a) Suppose that AABC is right-angled at B and has AB = 8. (n + 1)(n + 4), where n is a positive integer. Determine the number of positive integers n < 100 000 for which the length of side BC is also an integer. AC =

n(n + 1) and (a) Suppose that AABC is right-angled at B and has AB = 8. (n + 1)(n + 4), where n is a positive integer. Determine the number of positive integers n < 100 000 for which the length of side BC is also an integer. AC =

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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8. (a) Suppose that AABC is right-angled at B and has AB = n(n + 1) and AC = (n + 1)(n + 4), where n is a positive integer. Determine the number of positive integers n < 100 000 for which the length of side BC is also an integer. (b) Determine all real values of x for which ✓log2x log₂ (4x) +1+ log₂x log2 V X 64. +9=4
Transcribed Image Text:8. (a) Suppose that AABC is right-angled at B and has AB = n(n + 1) and AC = (n + 1)(n + 4), where n is a positive integer. Determine the number of positive integers n < 100 000 for which the length of side BC is also an integer. (b) Determine all real values of x for which ✓log2x log₂ (4x) +1+ log₂x log2 V X 64. +9=4
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8. (a) Suppose that AABC is right-angled at B and has AB = n(n + 1) and AC = (n + 1)(n + 4), where n is a positive integer. Determine the number of positive integers n < 100 000 for which the length of side BC is also an integer. (b) Determine all real values of x for which ✓log2x log₂ (4x) +1+ log₂x log2 V X 64. +9=4
Transcribed Image Text:8. (a) Suppose that AABC is right-angled at B and has AB = n(n + 1) and AC = (n + 1)(n + 4), where n is a positive integer. Determine the number of positive integers n < 100 000 for which the length of side BC is also an integer. (b) Determine all real values of x for which ✓log2x log₂ (4x) +1+ log₂x log2 V X 64. +9=4
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