Hence, the number is 5.
Further explanation:
Let x be a positive integer
Then
One less than a positive number will be written as: x-1
Three more than that number = x+3
According to the statement
One less than a positive number times three more than that number is 32
The equation will be:
[tex](x-1)(x+3)=32\\x(x+3)-1(x+3)=32\\x^2+3x-x-3=32\\x^2+2x-3-32=0\\x^2+2x-35=0\\Factorizing\\x^2+7x-5x-35=0\\x(x+7)-5(x+7)=0\\(x+7)(x-5)=0\\So,\\x+7=0\\x=-7\\x-5=0\\x=5[/tex]
We get two values for x, -7 and 5
But it is mentioned in the question that the number is positive, so the required number is 5.
Verification:
(x-1)(x+3)=32
(5-1)(5+3)=32
4*8=32
32=32
Hence, the number is 5.
Keywords: Quadratic equation, Factorization
Learn more about quadratic equations at:
- brainly.com/question/12973601
- brainly.com/question/13063819
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