Question

Two fractions are such that their product is ­2/5 and sum is 1/15. What are the two fractions.

A) 4/3, ­-3/10 B) 2/7, -­7/5 C) 4/7, ­-7/10 D) 2/3, ­-3/5

Answer 1

${\huge{\underline {\sf{\green {Answer:}}}}}$

${\underline {\rm{\purple {Given:}}}}$

• Product of two fractions is $\dfrac{-2}{5}$
• Sum of the two fractions is $\dfrac{1}{5}$

${\underline {\rm{\pink{Find:}}}}$

• The two numbers

${\underline {\rm{\purple {Solution:}}}}$

➮ Let the two fractions be x and y

➮ Two fractions are such that their product is $\dfrac{-2}{5}$ and $\dfrac{1}{5}$

➮Wee can write as ,

• xy = -2/5
• x + y = 1/15

In Product :

➳ y = (1/15) - x

In Addition :

➳ xy = (x/15) - x2 [Multiplying both sides by x]

Substituting the value of xy

➳ $\dfrac {x}{15} - {x}^{2} = [tex]\dfrac{-2}{5}$

➳ $\dfrac {x-15 × {x}^{2}}{15} - {x}^{2}= [tex]\dfrac{-2}{5}$

➳ x-15 × {x}^{2} = -6

➳ 15 × {x}^{2} - x - 6 = 0

➳15 × {x}^{2} - 10x + 9x - 6 = 0

➳5x(3x - 2) + 3(3x - 2) = 0

➳ (3x - 2)(5x + 3) = 0

Then, x = $\dfrac{2}{3}$ or x = $\dfrac{-3}{5}$

So ,y $\dfrac{1}{15}$ - $\dfrac{2}{3}$ = $\dfrac{-3}{5}$

∴ The two fraction are $\dfrac{2}{3}$ and $\dfrac{-3}{5}$

So, option d) 2/3, ­-3/5 is correct!

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