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4 years ago

For #23-24, translate and solve.

Mathematics

1 answer:

docker41 [41]4 years ago

4 0

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:

$(x-1)(x+3)=32\\x(x+3)-1(x+3)=32\\x^2+3x-x-3=32\\x^2+2x-3-32=0\\x^2+2x-35=0\\Factorizing\\x^2+7x-5x-35=0\\x(x+7)-5(x+7)=0\\(x+7)(x-5)=0\\So,\\x+7=0\\x=-7\\x-5=0\\x=5$

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:

#LearnwithBrainly

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