Question 520673: The product of two consecutive odd whole numbers is one less than five times their sum. Find the whole numbers Answer by Maths68(1474) (Show Source):
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One odd integer = x+1
Other odd integer = x+3
Given Condition
(x+1)(x+3)=5((x+1)+(x+3))-1
x^2+3x+x+3=5(x+1+x+3)-1
x^2+4x+3=5(2x+4)-1
x^2+4x+3=10x+20-1
x^2+4x+3=10x+19
x^2+4x-10x+3-19=0
x^2-6x-16=0
x^2-8x+2x-16=0
x(x-8)+2(x-8)=0
(x-8)(x+2)=0
x-8=0 or x+2=0
x=8 or x=-2 (inadmissible)
x=8
One odd integer = x+1 = 8+1=9
Other odd integer = x+3 = 8+3 = 11
Check
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Product of integers = 5 (sum of integers) -1
9*11=5(9+11)-1
99=5(20)-1
99=100-1
99=99
