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The square of the third of three consecutive integers is equal to twenty-five more than the product of the first two. What are the integers?
Wiki User
∙ 13y ago
Let the three consecutive integers be a, b, & c. Square of c is 25 more than a*b:
c2 = 25 + a*b; also the integers are consecutive, so a+1 = b & b+1 = c
put a & b in terms of c, so b = c-1 & a = b-1 = c-2, substitute these into original equation:
c2 = 25 + (c-2)*(c-1) = 25 + c2 - 3*c +2 --> c2 = 27 + c2 - 3*c --> 0 = 27 - 3*c
c = 9 and from the 'consecutive' equations: b = 8& a = 7
Substitute these values back into the original equation to make sure it works.
92 = 81 and 8*7 = 56. 81 is 25 more than 56.
Wiki User
∙ 13y ago
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hi
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