Im thinking of two proper fractions whose sum is 1912 and whose product is 58. Determine thefractions, and state them in simplest form.

Step 1 Let two fractions are a and b. Then according to question: a+b=1912 .....(1) And ab=58 .....(2) Step 2 Now using formula (a−b)2=(a+b)2−4ab (a−b)2=19122−458 (a−b)2=361144−52=361−360144 (a−b)2=1144 (a−b)=112 or (a−b)=−112 Step 3 If (a−b)=112 and (a+b)=1912 Then a=56 and b=34 If (a−b)=−112 and (a+b)=1912 Then a=34 and b=56

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facas9

Answered question

2021-09-30

Im thinking of two proper fractions whose sum is

\frac{19}{12}

and whose product is

\frac{5}{8}

. Determine thefractions, and state them in simplest form.

Answer & Explanation

cyhuddwyr9

Skilled2021-10-01Added 90 answers

Step 1
Let two fractions are a and b.
Then according to question:

a + b = \frac{19}{12}

.....(1)
And

a b = \frac{5}{8}

.....(2)
Step 2
Now using formula

{(a - b)}^{2} = {(a + b)}^{2} - 4 a b

{(a - b)}^{2} = {\frac{19}{12}}^{2} - 4 \frac{5}{8}

{(a - b)}^{2} = \frac{361}{144} - \frac{5}{2} = \frac{361 - 360}{144}

{(a - b)}^{2} = \frac{1}{144}

(a - b) = \frac{1}{12} or (a - b) = - \frac{1}{12}

Step 3
If

(a - b) = \frac{1}{12} and (a + b) = \frac{19}{12}

Then

a = \frac{5}{6} and b = \frac{3}{4}

(a - b) = - \frac{1}{12} and (a + b) = \frac{19}{12}

Then

a = \frac{3}{4} and b = \frac{5}{6}

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