Question

The product of two fractions is $\frac{5}{27}$ and their difference is $\frac{11}{18}$.. Find the two fractions.

Answer 1

Let , be the dfraction are =x and y

Now as per question $x\times y=\frac{5}{27}$ …(1)

$x-y=\frac{11}{18}$ …..(2)

From equation (1) put the value of x in equation (2)

$y(\frac{11}{18}+y)=\frac{5}{27}$

$\frac{11y}{18}+y^2=\frac{5}{27}$

Multiply by 54 on both sides

$33y+$ 54$y^2=10$

$54y^2+33y-10=0$

Now by quadratic formula

$y=\frac{-33\pm \sqrt{{33}^2-4\times 54\times (-10)}}{2\times 54}$

$\frac{-33\pm \sqrt{3249}}{2\times 54}=\frac{-33\pm 57}{2\times 54}$

$y=\frac{-33+57}{2\times 54},\frac{-33-57}{2\times 54}$

$=\frac{41}{108},\frac{-90}{2\times 54}$

$=\frac{41}{108},\frac{-15}{18}$

Consider y= $\frac{41}{108}$

Put the value of y in equation (2)

$x-\frac{41}{108}=\frac{11}{18}$

$x=\frac{11}{18}+\frac{41}{108}=\frac{107}{108}$

Hence, $\frac{107}{108}$ ,$\frac{41}{108}$ are required answer