Question

divide 42 into two parts so that one part is twice the other​

Answer 1

Hey mate!!!

Here's your answer :

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Words have meaning. Some of the way the words are used together make no sense, but this looks like a problem that can be fixed.

Divide 42 into two equal parts

42=a+a, with solution a=21. Done.

Divide 42 into two … parts ignoring the demand to make them equal.

Presumably this means 42 is the sum of two variables.

42=R+S

… such that one part is equal to the square of the other part

Presumably this means the two variables are related to each other.

S=R2

… in quadratic equations with one variable.

First we write one variable in terms of the other.

42=R+S⇒S=(42−R)

Then we substitute in that expression for one variable and simplify in terms of that other variable.

S=R2⇒42−R=R2⇒R2+R−42=0

Alternately, we could start with S=R2 as the substitution and end up again with R2+R−42=0.

After interpreting the question in terms of math, we next need to interpret the solutions of R2+R−42=0 in terms of the original problem.

The two (mutually exclusive) solutions are R=−7 and R=6. This means the solutions to the first part are (R,S)=(−7,49) and (R,S)=(6,36).

Does R=−7 make sense? That means 42=(−7)+49, which is true, but is −7 a part of 42? That depends on what you think “part” means. Some might say “no, only positive numbers can be part of positive numbers”. Some might say “since we use negative numbers all the time, there is no reason why they can’t be valid ‘parts’.”

Does R=6 make sense? That means 42=6+36, which is true, and 6 is a part of 42 as people understand the natural number.

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Answer 2

Hope it helps you...

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