Mathematics: Is the product of two mixed numbers less than,between, or greater than the two factors

For this case we have the following solutions:Then, the factorized equation is of the form:We apply distributive property:The equation is...

Is the product of two mixed numbers less than,between,

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lorriegoodman3483

03.01.2022

Mathematics

The product of two numbers is greater than the two factors.
for example if we take two number 2 and 4. The product of 2 and is 2 x 4 = 8
now 8 is greater than 2 and also greater than 4. 8 is not less than 2 or less than 4 and not between the 2 and 4. So, the product of two number is greater than two factors. There is an exception also that the numbers will be positive.

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Ответ:

kcdavis318

22.08.2020

Mathematics

For this case we have the following solutions:

$x_ {1} = 1 + \sqrt {5}\\x_ {2} = 1- \sqrt {5}$

Then, the factorized equation is of the form:

$(x- (1+ \sqrt {5})) (x- (1- \sqrt {5})) = 0\\(x-a) (x-b) = 0$

We apply distributive property:

$x ^ 2-bx-ax + ab = 0\\x ^ 2- (1- \sqrt {5}) x- (1+ \sqrt {5}) x + (1+ \sqrt {5}) (1- \sqrt {5}) = 0\\x ^ 2-x + \sqrt {5} x-x- \sqrt {5} x + (1 ^ 2- \sqrt {5} + \sqrt {5} - (\sqrt {5}) ^ 2) = 0\\x ^ 2-2x + (1-5) = 0\\x ^ 2-2x-4 = 0$

The equation is x ^ 2-2x-4

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Is the product of two mixed numbers less than,between, or greater than the two factors

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